Application of Queueing-Theoretic Methods in Operations Research

  • N. P. Buslenko
  • A. P. Cherenkov
Part of the Progress in Mathematics book series (PM, volume 11)


One of the most important areas to come under the jurisdiction of cybernetics is that which is commonly termed “operations research.” By the word “operation” in the given context we mean a set of activities directed toward the attainment of a particular objective and implemented in the form of a suitable algorithm.


Service Time Traffic Flow Modeling Algorithm Traffic Light Queueing System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    Aliev, G. A., Modeling of systems by the bulk-service method, Usp. Mat. Nauk, 20 (4): 198–199 (1965).Google Scholar
  2. 2.
    Aliev, G. A., Buslenko, N. P., Klimov, G. P. and Nazarenko, A. I„ Modeling of the industrial operation of an automated machine for the furnace welding of pipe, in: Problems of Cybernetics, No. 9, Fizmatgiz, Moscow (1965), pp. 211–240.Google Scholar
  3. 3.
    Akhmedov, A., A technique for modeling the operation of a certain class of queueing systems, Usp. Mat. Nauk., 19 (5): 198–200 (1964).Google Scholar
  4. 4.
    Basharin, G. P., Final probabilities of a multidimensional Markov process describing the action of certain two-stage telephone system with losses operating in the free-hunting mode, Dokl. Akad. Nauk SSSR, pp. 452–458 (1960).Google Scholar
  5. 5.
    Basharin, G. P., Probability-theoretic study of a two-stage telephone system with losses operating in the free-hunting mode, Dokl. Akad. Nauk SSSR, 121 (1): 101–104 (1958).Google Scholar
  6. 6.
    Basharin, G. P., On the multivariate limiting distribution of the numbers of busy lines in the second-stage switchboards of a telephone system with losses, Dokl. Akad. Nauk SSSR, 121 (2): 280–283 (1958).Google Scholar
  7. 7.
    Basharin, G. P., Derivation of sets of equations of state for two-stage telephone circuits with losses, Élektrosvyaz’, No. 1, pp. 56–64 (1960).Google Scholar
  8. 8.
    Basharin, G. P., Limiting distribution of the busy time of a fully-accessible trunk, Teor. Veroyat. i Prim., 5 (2): 246–252 (1960).MATHGoogle Scholar
  9. 9.
    Basharin, G. P., Queueing Problems in Telephone Theory, Nauka, Moscow (1968).Google Scholar
  10. 10.
    Basharin, G. P. and Shval’b, V. P., Digital computer modeling of the operation of switching systems by the Monte Carlo method, Izv. Akad. Nauk SSSR, Otc. Tekh. Nauk Énerg. i Avtomatika, No. 3, pp. 143–153 (1962).Google Scholar
  11. 11.
    Basharin, G. P. and Shneps, M. A., Survey of the latest work in telephone communication theory, Radiotekhnika, 6 (5): 43–48 (1963).Google Scholar
  12. 12.
    Belostotskii, A. A. and Val’denberg, Yu. S., Statistical modeling of the operation of a section of a metallurgical combine, Izv. Akad, Nauk SSSR, Tekh. Kibernetika, No. 6, pp. 38–46 (1964).Google Scholar
  13. 13.
    Bend, V. E., Mathematical Principles of Telephone Communication Theory [Russian translation], Svyaz’, Moscow (1968), 291 pages.Google Scholar
  14. 14.
    Bronshtein, O. I., Raikin, A. L. and Rykov, V. V., A single-line queueing system with losses, Izv. Akad. Nauk SSSR, Tekh. Kibernetika, No. 4, pp. 45–51 (1965).Google Scholar
  15. 15.
    Buslenko, N. P., Solution of problems in queueing theory by digital computer simulation, in: Problems of Information Transmission, No. 9, Izd. AN SSSR, Moscow (1961), pp. 48–69.Google Scholar
  16. 16.
    Buslenko, N.’P., Digital computer simulation of production processes, Dokl. Akad. Nauk SSSR, 144 (5): 1003–1006 (1962).Google Scholar
  17. 17.
    Buslenko, N. P., Digital computer simulation of production processes, in: Problems of Cybernetics, No. 9, Fizmatgiz, Moscow (1963), pp. 189–310.Google Scholar
  18. 18.
    Buslenko, N. P., On the theory of complex systems, Izv. Akad. Nauk SSSR, Tekh. Kibernetika, No. 5, pp. 7–18 (1963).Google Scholar
  19. 19.
    Buslenko, N. P., Solution of queueing-related problems by the Monte Carlo method, Proc. Fourth All-Union Mathematics Congress, 1961, Vol. 2, Nauka, Leningrad (1964), pp. 326–329.Google Scholar
  20. 20.
    Buslenko, N. P., Mathematical Modeling of Production Processes on Digital Computers, Nauka, Moscow (1964), 362 pages.Google Scholar
  21. 21.
    Buslenko, N. P„ Golenko, D. I., Sobol’, I. M., Sragovich, V. G. and Sheider, Yu. A., The Statistical Trial-and-Error (Monte Carlo) Method, Fizmatgiz, Moscow (1962), 331 pages.Google Scholar
  22. 22.
    Buslenko, N. P. and Shreider, Yu. A., The Statistical Trial-and-Error (Monte Carlo) Method and its Implementation on Digital Computers, Fizmatgiz, Moscow (1961), 226 pages.Google Scholar
  23. 23.
    Gnedenko, B. V., On the average down time of machines in multistage operation, Izv. Khlopchatobum. Prom., 11: 15–18 (1934).Google Scholar
  24. 24.
    Gnedenko, B. V. and Zubkov, M.N., Determination of the optimum number of ship moorings, Morskoi Sb., No. 6, pp. 30–39 (1964).Google Scholar
  25. 25.
    Gnedenko, B. V. and Kovalenko, I. N., Lectures on Queueing Theory, Nos. 1–3, Kiev (1963).Google Scholar
  26. 26.
    Golenko, D. 1., Levin, N. A., Mikhel’son, V. S. and Naidov-Zhelezov, Ch. G., Automation of the Planning and Administration of New Developments, Zvaigzne, Riga (1966), 191 pages.Google Scholar
  27. 27.
    Gubanov, V., On the rational selection of automobile parking space, Sb. Trud. Soiskatelei i Aspirantov, Moskov. Vyssh. i Sredn. Spets. Obrazov. Kazakh. SSR, 1 (1): 58–62 (1963).Google Scholar
  28. 28.
    Guseinov, B. T., On the waiting time of ships taking on cargo, Izv. Azerbaidzhan. SSR, Ser. Fiz.-Tekh. i Mat. Nauk, No. 2, pp. 49–54 (1967).Google Scholar
  29. 29.
    Kalashnikov, V. V., A queueing system with “inaccessibility intervals, ” Izv. Akad. Nauk SSSR, Tekh. Kibernetika, No. 6, pp. 57–63 (1966).Google Scholar
  30. 30.
    Klimov, G. P., Stochastic Queueing Systems, Nauka, Moscow (1966), 243 pages.Google Scholar
  31. 31.
    Klimov, G. P. and Alley, G. A., Computer solution of a problem in queueing theory by the Monte Carlo method, Zh. Vychisl. Mat, i Mat. Fiz., 1 (5): 933–935 (1961).Google Scholar
  32. 32.
    Klimov, G. P. and Kurilov, V. I., Modeling of a class of queueing systems, Sb. Rabot Vychisl. Tsentra Moskov. Univ., No. 3, pp. 398–408 (1965).Google Scholar
  33. 33.
    Kobozev, V. V. and Nazarenko, A. I., Mathematical modeling of the operation of a sorting and rolling mill, Izv. Akad, Nauk SSSR, Tekh. Kibernetika, No. 2, pp. 12–23 (1964).Google Scholar
  34. 34.
    Kovalenko, A. I. and Rostomyan, K. E., On the mathematical-logical modeling of livestock production processes, Transactions of the Computer Center of the Armenian SSR and Yerevan State University: Problems of Statistics and Economic Cybernetics, Yerevan (1965).Google Scholar
  35. 35.
    Kovalenko, I. N., Some limited queueing problems, Teor. Veroyat. i Prim., 6 (2): 222–228 (1961).MathSciNetGoogle Scholar
  36. 36.
    Kovalenko, I. N., Queueing theory, in: Probability Theory, 1963 ( Itogi Nauki, VINITI AN SSSR ), Moscow (1965), pp. 73–125.Google Scholar
  37. 37.
    Kovalenko, I. N., Analytical methods in queueing theory, in: Cybernetics in the Service of Communism, Vol. 2, Énergiya, Moscow-Leningrad (1964), pp. 325–338.Google Scholar
  38. 38.
    Kaufmann, A. and Cruon, R., Queueing Theory (Theory and Applications) (Russian translation from French), Mir, Moscow (1965), 302 pages.Google Scholar
  39. 39.
    Kruchinina, É, V., Investigation of automobile traffic as a complex system by the method of statistical modeling, Trans. Moscow Institute of Statistical Economics, Moscow (1967).Google Scholar
  40. 40.
    Kurt-Umerov, V. O., A mathematical model for the prognosis of gradual failure of the elements of a system, Avtomat. i Telemekhan., No. 2, pp. 142–146 (1966).Google Scholar
  41. 41.
    Lanin, M. I., Calculation of the message loss probability in centralized control systems, Avtomat. i Telemekhan., 23 (3): 321–330 (1962).Google Scholar
  42. 42.
    Luik, I. A., Certain principles of the engineering operation of machine stock in: The Reliability of Complex Engineering Systems, Sov. Radio (1966), pp. 56–59.Google Scholar
  43. 43.
    Maizlin, I. E. and Nikolaeva, L. P., Determination by the statistical trial-anderror method of the distribution of the completion time of developments in network planning, Izv. Akad. Nauk SSSR, Tekh. Kibernetika, No. 3, pp. 97–103 (1965).Google Scholar
  44. 44.
    Margulis, Kh. Sh. and Fridman, G. Ya., Statistical modeling of a particular class of complex systems, Dokl. Akad. Nauk SSSR, 168 (2): 296–299 (1966).Google Scholar
  45. 45.
    Mar’yanovich, T. P., Generalization of the Erlang formulas to the case of device breakdown and renewal, Ukrainsk. Mat. Nauk, 12 (3): 279–286 (1960).Google Scholar
  46. 46.
    Mar’yanovich, T. P., Reliability of systems under reserve demand, Dopovidi AN Ukrain. SSR, No. 7, pp. 850–853 (1961).Google Scholar
  47. 47.
    Mar’yanovich, T. P., Reliability of systems with.-nixed reserves, Dopovidi AN Ukrain. SSR, No. 8, pp. 994–997 (1961).Google Scholar
  48. 48.
    Mebuke, B. K. and Tsereteli, V. B., An optimal priority distribution problem in a single-channel limited-length queueing system, Sakartvelos Politeknikuri Inst., Shromebi, Trudy Gruz. Politekh. Inst., No. 2 (122), pp. 231–236 (1968).Google Scholar
  49. 49.
    Mudrov, V. I., A queue with “impatient” customers and variable service time depending linearly on the waiting time of the customer in the queue, Problems of Cybernetics, No. 5, Fizmatgiz, Moscow (1961), pp. 283–285.Google Scholar
  50. 50.
    Tadatosi, Nisimura, Sample calculation of the number of harbor installations by means of queueing theory, Tech. Rep. Fuji Iron and Steel Co., 10(4): 602612 (1962).Google Scholar
  51. 51.
    Sevast’yanov, B. A., The Erlang formulas in telephone theory for an arbitrary distribution of the time of an established call, Proc. Third All-Union Mathematics Congress, Vol. 4, Izd. AN SSSR, Moscow (1969), pp. 68–70.Google Scholar
  52. 52.
    Sevast’yanov, B. A., Influence of the capacity of bins on the down time of an automatic line of machines, Teor. Veroyat. i Prim., 7 (4): 438–447 (1962).MathSciNetGoogle Scholar
  53. 53.
    Takacs, L., Some probability questions in the thoery of telephone traffic [Russian translation], Period. Sb. Perevod. Inostr. Stat., 4 (6): 93–144 (1960).Google Scholar
  54. 54.
    Tsutomu, Tikuse, Operations research in the planning of the capacity of bus stations, Rep. Fac. Engng. Jamanashi Univ., No. 13, pp. 128–131 (1962).Google Scholar
  55. 55.
    Fidrikh, I., Description of an algorithm for the solution of queueing problems by the statistical trial-and-error method, Dokl. Akad. Nauk SSSR, 153 (4): 779–782 (1963).MathSciNetGoogle Scholar
  56. 56.
    Khinchin, A. Ya., Mathematical methods of queueing theory, Trudy Mat. Inst. Akad. Nauk SSSR, 49: 1–129 (1955).Google Scholar
  57. 57.
    Kadzuo, Hirose, Calculations of dock loading and unloading operations by the Monte Carlo method, Keiei Kagaku, 5 (3): 186–191 (1962).Google Scholar
  58. 58.
    Khoult, Ch. S., Priority rules minimizing losses due to product delays in queues in the scheduling of machine operations, in: Scheduling, Progress, Moscow (1966), pp. 109–122.Google Scholar
  59. 59.
    Shneps, M. A., Computer study of single-stage partially-accessible telephone systems, in: Problems of Information Transmission, No. 12, Izd. AN SSSR, Moscow (1963), pp. 109–123.Google Scholar
  60. 60.
    Shneps, M. A., Application of Markov chains for the investigation of telephone systems with losses, in: Problems of Information Transmission, No. 12, Izd. AN SSSR, Moscow (1963), pp. 124–134.Google Scholar
  61. 61.
    Shneps, M. A., Application of the method of nested Markov chains to the modeling of queueing systems with losses, Uch. Zap. Latv. Univ., 47: 261–266 (1963).Google Scholar
  62. 62.
    Haruo, Akumaru, Optimum design of switching systems, Rev. Elec. Commun. Lab., 10 (7–8): 385–401 (1962).Google Scholar
  63. 63.
    Bailey, N.T.I., Study of queues and appointment systems in outpatient departments with special reference to waiting times, J. Roy. Statist. Soc., B14 (1): 185–199 (1952).Google Scholar
  64. 64.
    Bailey, N. T. J., Queueing for medical care, Appl. Statist. 3 (2): 137–145 (1954).MATHGoogle Scholar
  65. 65.
    Bailey, N. T. J., Statistics in hospital planning and design, Appl. Statist., 5 (3) (1956).Google Scholar
  66. 66.
    Bailey, N. T. J., Operational research in hospital planning and design, Oper-at. Res, Quart., 8 (3): 149–157 (1957).Google Scholar
  67. 67.
    Brtfai, P. and Dobo, A., Eqy közlekedési problémáról, Magyar Tud. Akad. Mat. és Fiz. Tud. Oszt. Közl., 11 (3): 263–271 (1961).Google Scholar
  68. 68.
    Barlett, M. S., Some problems associated with random velocity, Publ. Inst. Statist. Univ. Paris, 6 (4): 261–270 (1957).Google Scholar
  69. 69.
    Bend, V. E., On queues with Poisson arrivals, Ann. Math. Statistics, 28 (3): 670–677 (1957).CrossRefGoogle Scholar
  70. 70.
    Bend, V. E., On trunks with negative exponential holding times serving a renewal process, Bell Syst. Tech. J., 38 (1): 211–258 (1959).Google Scholar
  71. 71.
    Bend, V. E., A “renewal” limit theorem for general stochastic processes, Ann. Math. Statist., 33 (1): 98–113 (1962).MathSciNetCrossRefGoogle Scholar
  72. 72.
    Ben-Israel, A, and Naor, P., A problem of delayed service (I), J. Roy. Statist. Soc., B22 (2): 245–269 (1960).MathSciNetMATHGoogle Scholar
  73. 73.
    Benson, F. and Gregory, G., Closed queueing systems: a generalization of the machine interference model, J. Roy. Statist. Soc., B23 (2): 385–393 (1961).Google Scholar
  74. 74.
    Berline, C. G.,Applications des méthodes de la recherche operationelle l’industrie pétrolière, Actes 2 Congr. Internat. Rech. Opérat., Aix-en-Provence, 1960, Paris, (1961), pp. 353–354, Discussion pp. 759–763.Google Scholar
  75. 75.
    Blom, G., Hierarchical birth and death processes, I: Theory, Biometrika, 47(3–4): 47 (3–4): 235–244 (1960).Google Scholar
  76. 76.
    Blom, G.,Hierarchical birth and death processes, II: Applications, Biometrika, 47(3–4): 245–252 (1960).Google Scholar
  77. 77.
    Blumstein, A., The landing capacity of a runway, Operas. Res., 7 (6): 752–763 (1959).Google Scholar
  78. 78.
    Blumstein, A., The operations capacity of a runway used for landings and takeoffs, Actes 2 Congr. Internat. Rech. Operat., Aix-en-Provence, 1960, Paris (1961), pp. 657–672, Discussion pp. 776–778.Google Scholar
  79. 79.
    Borel, E., Sur l’emploi du theorème de Bernoulle pour faciliter le calcul d’une de coefficients, Compt. Rend., 214 (3): 452 (1942).MathSciNetGoogle Scholar
  80. 80.
    Breiman, L., The Poisson tendency in traffic distribution, Ann. Math. Statist., 34 (1): 308–311 (1963).MathSciNetMATHCrossRefGoogle Scholar
  81. 81.
    Brettmann, E., Der Einfluss von Verspätungen auf die Leistungsfähigkeit einer eingleisigen Strecke in Abhängigkeit von der Streckenlängen, Arch. Eisenbahn-tech., No. 16, pp. 63–98 (1962).Google Scholar
  82. 82.
    Brigham, G., On a congestion problem in an aircraft factory, J. Operat. Res. Soc. Amer., 3: 412–428 (1955).MathSciNetCrossRefGoogle Scholar
  83. 83.
    Buckley, D. J. and Wheeler, R. C., Some results for fixed-time traffic signals, J. Roy. Statist. Soc., B26 (1): 133–140 (1964).MathSciNetMATHGoogle Scholar
  84. 84.
    Chandler, R. E., Herman, R. and Morroll, E. W„ Traffic dynamics: studies in car following, Operat. Res., 6 (2): 165–184 (1958).Google Scholar
  85. 85.
    Chartrand, M., The Design of Cafeteria Counters, Norton Company Rep., Worcester, Mass. (1957).Google Scholar
  86. 86.
    Clunies-Ross, C. and Husson, S.S., Statistical techniques in circuit optimization, Proc. Nat. Electron. Conf., Chicago, Ill, 1962, Chicago, 1ll. (1962), pp. 325–334.Google Scholar
  87. 87.
    Cohen, J. W., Einige beschouwingen over stochastische processen in het wegverkeer, Ingenieur (Netherlands), 74(48): V 39 - V47 (1962).Google Scholar
  88. 88.
    Crane, R. R., Brown, F. B. and Blanchard, R. O., An analysis of railroad classification yards, J. Opérat.,Res. Soc. Amer., 2 (2): 262 (1955).MATHGoogle Scholar
  89. 89.
    Craven, B. D., Some results for the bulk service queue, Austral. J. Statist., 5 (2): 49–56 (1963).MathSciNetMATHGoogle Scholar
  90. 90.
    Darroch, J. N., On the traffic-light queue, Ann. Math. Statist., 35 (1): 380–388 (1964).MathSciNetMATHCrossRefGoogle Scholar
  91. 91.
    Darroch, J. N., Newell, G. F. and Morris, R. W. J., Queues for vehicle-actuated traffic lights, Operat. Res., 12 (6): 882–895 (1964).Google Scholar
  92. 92.
    Delcourt, J., Equipement d’une station de pompage, Rev. Statist. Appl. 1 (2): 77–85 (1959).Google Scholar
  93. 93.
    Delcourt, J., Problèmes de la congestion dans un por pétrolier, Actes 2 Congr, Internat. Rech. Opérat. Aix-en-Provence, 1960, Paris (1961), pp. 365–375, Discussion pp. 759–763.Google Scholar
  94. 94.
    Disney, R. L., Some results of multichannel queueing problems with ordered entry–an application to conveyer theory, J. Industr. Engng., 14 (2): 105–108 (1963).Google Scholar
  95. 95.
    Dobbie, J. M., A double-ended queueing problem of Kendall, Operat. Res., 9 (5): 755–757 (1961).MATHGoogle Scholar
  96. 96.
    Dunne, M. C. and Potts, R. B., Algorithm for traffic control, Operat. Res., 12 (6): 870–881 (1964).MathSciNetMATHGoogle Scholar
  97. 97.
    Edel, L. C., A reply to comments by James M. Dobbie, Operat. Res., 4(3): 614619 (1956).Google Scholar
  98. Edie, L. C., Gasiz, D. C., Helly, W., Herman, R. and Rothery, R., Third International Symposium on the Theory of Traffic Flow, Operat. Res., 13 (6): 1045–1051 (1965).Google Scholar
  99. 99.
    Eisen, M., On switching problems requiring queueing theory in computer-based systems, IRE Trans. Communications Systems, 10 (3): 299–303 (1962).MathSciNetGoogle Scholar
  100. 100.
    Ekberg, S., Determination of the traffic-carrying properties of gradings with the aid of some derivative-parameters of telephone traffic distribution functions, Abhandl. Mkt. Teknol. Kungl. Tek. Högsk,, Stockholm, No. 126 (1958), 93 pages.Google Scholar
  101. 101.
    Elldin, A., Further studies on gradings with random hunting, Ericsson Tech., 13 (2): 175–257 (1957).Google Scholar
  102. 102.
    Engset, T., Die Wahrscheinlichkeitsrechnung zur Bestimmung der Wähleranzahl in automatischen Fernsprechämtern; Elektrotech. Z., 31: 304–306 (1918).Google Scholar
  103. 103.
    Erlang, A. K., Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges, The Post Office Electr. Engng. J., 10: 189–197 (1918).Google Scholar
  104. 104.
    Evans, D.H., Herman, R. and Weiss, G. H., The highway merging and queueing problem, Operat. Res., 12 (6): 832–857 (1964).MathSciNetMATHGoogle Scholar
  105. 105.
    Ferrer, M. S., Tiempos y movimientos; inactividades; caso de máquinas y trabajadores distintos, Bol. Estadist., Suppl. 16 (8): 33–45 (1956).Google Scholar
  106. 106.
    Finch, P. D., Cyclic queues with feedback, J. Roy. Statist. Soc., B21 (1): 153–157 (1959).MathSciNetMATHGoogle Scholar
  107. 107.
    Finch, P. D., The transient behaviour of a coincidence variate in telephone traffic, Ann. Math. Statist., 32 (1): 230–235 (1961).Google Scholar
  108. 108.
    Flagle, C. D., Operations research in the health services, Operat. Res., 10 (5): 591–603 (1962).Google Scholar
  109. 109.
    Flagle, C. D., The Problem of Organization for Hospitals; Inpatient Care, Reprints, Pergamon Press Ltd., London (1959).Google Scholar
  110. 110.
    Fortet, R., Théorie du trafic de convoi, Rev. Franc. Rech. Operat., 6(25): 337–360 (1962).Google Scholar
  111. 111.
    Foster, F. G., Queues with batch arrivals (I), Acta Math. Acad. Sci. Hung., 12 (1–2): 1–10 (1961).MathSciNetMATHCrossRefGoogle Scholar
  112. 112.
    Galliher, H. P. and Wheeler, R. C., Nonstationary queueing probabilities for landing congestion of aircraft, Operat. Res., 6 (2): 264–275 (1958).MathSciNetGoogle Scholar
  113. 113.
    Garreau, G. A., The use of queueing theory, Trans. Soc. Instrum. Technol., 15 (3): 190–493 (1963).Google Scholar
  114. 114.
    Gaver, D. P., Jr., A waiting line with interrupted service, including priorities, J. Roy. Statist. Soc., B24 (1): 73–90 (1962).Google Scholar
  115. 115.
    Gaver, D. P., Jr., Accommodation of second-class traffic, Operat. Res., 11 (1): 72–87 (1963).MATHGoogle Scholar
  116. 116.
    Gaver, D. P., Jr., A probability problem arising in reliability and traffic studies, Operat. Res., 12 (4): 534–542 (1964).MathSciNetMATHGoogle Scholar
  117. 117.
    Gazis, D. C., Herman, R, and Rothery, R. W., Nonlinear follow-the-leader models of traffic flow, Operat. Res., 9 (4): 545–567 (1961).MathSciNetMATHGoogle Scholar
  118. 118.
    Gazis, D. C., Herman, R. and Weiss, G. H., Density oscillations between lanes of a multilane highway, Operat. Res., 10 (5): 658–667 (1962).MATHGoogle Scholar
  119. 119.
    Gazis, D. C. and Weiss, G. H., Effects of random travel times on the design of traffic light progressions, J. Franklin Inst., 282 (1): 1–8 (1966).CrossRefGoogle Scholar
  120. 120.
    Geisler, M. A., Integration of modelling and simulation in organizational studies, in: Management Science Models and Techniques, Vol. 1, Pergamon, Oxford-London-New York-Paris (1960), pp. 139–147.Google Scholar
  121. 121.
    Ghosal, A., Queues in series, J. Roy. Statist. Soc., B24 (2): 359–363 (1962).MathSciNetMATHGoogle Scholar
  122. 122.
    Gordon, W. J. and Newell, G. F., Equilibrium analysis of a stochastic model of traffic flow, Proc. Cambridge Phil. Soc., 60 (2): 227–236 (1964).MathSciNetMATHGoogle Scholar
  123. 123.
    Goulcher, R., The application of queueing theory to batch manufacturing, Brit. Chem. Engng., 13 (3): 377–380 (1968).Google Scholar
  124. 124.
    Greenberg, H., Analysis of traffic flow, Operat. Res., 7 (1): 7–79 (1959).Google Scholar
  125. 125.
    Greenberger, M., The priority problem and computer time sharing, Management Sci., 12 (11): 888–906 (1966).MathSciNetCrossRefGoogle Scholar
  126. 126.
    Gupta, S. K., Queues with hyper-Poisson input and exponential service time distribution with state-dependent arrival and service rates, Operat. Res., 15 (5): 847–856 (1967).MATHGoogle Scholar
  127. 127.
    Haight, F. A., Queueing with balking, Biometrika, 33 (3–4): 360–369 (1957).MathSciNetMATHGoogle Scholar
  128. 128.
    Haight, F. A., Towards a unified theory of road traffic, Operat. Res., 6 (6): 813–826 (1958).Google Scholar
  129. 129.
    Haight, F. A., Queueing with reneging, Metrika, 2 (3): 186–197 (1959).MathSciNetMATHCrossRefGoogle Scholar
  130. 130.
    Haight, F. A., Overflow at a traffic light, Biometrika, 46 (3–4): 420–424 (1959).MathSciNetMATHGoogle Scholar
  131. 131.
    Haight, F. A., Expected utility for queues servicing messages with exponentially-decaying utility, Ann. Math. Statist., 32 (2): 587–593 (1961).MathSciNetMATHCrossRefGoogle Scholar
  132. 132.
    Haight, F. A., Mathematical Theories of Traffic Flow, Academic Press, New York (1963), 242 pages.Google Scholar
  133. 133.
    Haight, F. A., Annotated bibliography of scientific research in road traffic and safety, Operat. Res„ 12 (6): 976–1039 (1964).MathSciNetMATHGoogle Scholar
  134. 134.
    Hawkes, A. G., Queueing for gaps in traffic, Biometrika, 52(1–2): 79–85(1965).Google Scholar
  135. 135.
    Heathcote, C. R., The time-dependent problem for a queue with preemptive priorities Operat. Res., 7 (5): 670–680 (1959).MathSciNetMATHGoogle Scholar
  136. 136.
    Helly, W., Two stochastic traffic systems whose service times increase with occupancy, Operat. Res., 12 (6): 951–963 (1964).MathSciNetMATHGoogle Scholar
  137. 137.
    Henn, R., Die Behandlung betrieblicher Störungen and Staungen durch Übergangswahrscheinlichkeiten, Schweiz, Z. Volkswirtsch. and Statist., 96(1): 35–44 (1960)Google Scholar
  138. 138.
    Herman, R. and Weiss, G., Comments on the highway-crossing problem, Operat. Res., 9 (6): 828–840 (1961).MathSciNetMATHGoogle Scholar
  139. 139.
    Hill, L., The application of queueing theory to the span of control, J. Acad. Manag., 6 (1): 58–69 (1963).Google Scholar
  140. 140.
    Hillier, F. S., Economic models for industrial waiting-line problems, Management Sci., 10 (1): 119–130 (1963).CrossRefGoogle Scholar
  141. 141.
    Hirsch, W. M., Conn, J. and Siegel, C., A queueing process with an absorbing state, Commun. Pure Appl. Math., 14 (2): 137–153 (1961).MathSciNetMATHGoogle Scholar
  142. 142.
    Hochsteiner, O., Anwendung der Wahrscheinlichkeitslehre auf den Strassen-und Bahnverkehr, Wiss. Z. Hochschule Verkehrwesen Dresden, 6(1): 33–57 (1958–59).Google Scholar
  143. 143.
    Hodgson, V. and Hebble, T. L., Nonpreemptive priorities in machine interference, Operat. Res., 15 (2): 245–253 (1967).Google Scholar
  144. 144.
    Tsuruchiyo, Homma, On some fundamental traffic problems Yakohama Math. J., 5 (1): 99–114 (1957).MATHGoogle Scholar
  145. 145.
    Hooper, J. W. and Stoller, D. S., The aggregation of servicing facilities in queueing processes, Management Science Models and Techniques, Vol. 2, Pergamon, Oxford-London-New York-Paris (1960), pp. 316–325.Google Scholar
  146. 146.
    Hunt, G. C., Sequential arrays of waiting lines, Operat. Res., 4 (6): 674–683 (1956).Google Scholar
  147. 147.
    Jackson, J. R., Networks of waiting lines, Operat. Res., 5 (4): 518–521 (1957).Google Scholar
  148. 148.
    Jackson, J. R., Jobshop-like queueing systems, Management Sci., 10(1): 131142 (1963).Google Scholar
  149. 149.
    Jackson, R. R. P., Queueing systems with phase-type service, Operat. Res. Quart., 5 (4): 109–120 (1954).Google Scholar
  150. 150.
    Jackson, R. R. P., Random queueing processes with phase-type service, J. Roy. Statist. Soc., B18 (1): 129–132 (1956).MATHGoogle Scholar
  151. 151.
    Jeanniot, J. P. and Sandiford, P. J., Some airline applications of Monte Carlo system simulations, Information Processing, 1962, N. Holland Publ. Co., Amsterdam (1963), pp. 67–72.Google Scholar
  152. 152.
    Jensen, A„ Application of stochastic processes to an investment plan, Metroecon., 5: 129–137 (1953).Google Scholar
  153. 153.
    Jewell, W. S., Multiple entries in traffic, J. Soc. Industr. Appl. Math., 11 (4): 872–885 (1963).MathSciNetCrossRefGoogle Scholar
  154. 154.
    Jewell, W. S., Forced merging in traffic, Operat. Res., 12 (6): 858–869 (1964).MATHGoogle Scholar
  155. 155.
    Jorgensen, N. O., Determination of the capacity of road intersections by model testing, Ingeni(dren, C5 (3): 99–104 (1961).Google Scholar
  156. 156.
    Kalaba, R. E. and Juncosa, M. L., Communication-transportation networks, Naval Rec. Logist. Quart., 4 (3): 221–222 (1957).CrossRefGoogle Scholar
  157. 157.
    Karlin, S., Miller, R. G. and Prabhu, N. U., Note on a moving single server problem, Ann. Math. Statist., 30 (1): 243–246 (1959).MathSciNetMATHCrossRefGoogle Scholar
  158. 158.
    Kashyap, B. R. K., The double-ended queue with bulk service and limited waiting space, Operat. Res., 14 (5): 822–834 (1966).MathSciNetMATHGoogle Scholar
  159. 159.
    Kaufmann, A. and Cruon, R., Les phénomenes d’ attente (Théorie et applications), Dunod, Paris (1961), xiv + 274 pages, illustrated.Google Scholar
  160. 160.
    Tatsuo, Kawata, A problem in the theory of queues, Rep. Statist. Appl. Res. Union Japan. Scientists and Engrs., 3 (4): 122–129 (1955).Google Scholar
  161. 161.
    Keilson, J., The general bulk queue as a Hilbert problem, J. Roy. Statist. Soc., B24 (2): 344–358 (1962).MathSciNetMATHGoogle Scholar
  162. 162.
    Kendall, D. G., Some problems in the theory of queues, J. Roy. Statist. Soc., B13 (2): 151–185 (1951).MathSciNetMATHGoogle Scholar
  163. 163.
    Kesten, H. and Runnenburg, J. T., Priority in waiting-line problems (I, II), Proc. Koninkl. Nederl. Akad. Wetensch., A60(3): 312–324; 325–336 (1957); Indagationes Math., 19(3): 312–324; 325–336 (1957).MathSciNetGoogle Scholar
  164. 164.
    Kleinecke, D.C., Discrete-time queues at a periodic traffic light, Operat. Res., 12 (6): 809–814 (1964).MathSciNetMATHGoogle Scholar
  165. 165.
    Kleinrock, L. and Finkelstein, R. P., Time-dependent priority queues, Operat. Res., 15 (1): 104–116 (1967).MathSciNetMATHGoogle Scholar
  166. 166.
    Kmenta, J. and Joseph, M. E., A Monte Carlo study of alternative estimates of the Cobb-Douglas production function, Econometrica, 31 (3): 363–385 (1963).MATHCrossRefGoogle Scholar
  167. 167.
    Koenigsberg, E., Queueing with special service, Operat. Res., 4 (2): 213–220 (1956).Google Scholar
  168. 168.
    Keonigsberg, E., Cyclic queues, Operat. Res. Quart., 9 (1): 22–35 (1958).Google Scholar
  169. 169.
    Kometani, E., An abridged table for infinite queues, Operat Res., 7(3): 385393 (1959).Google Scholar
  170. 170.
    Kotler, P., The use of mathematical models in marketing, J. Market., 27(4): 31–41 (1963)Google Scholar
  171. 171.
    Kremser, H., Ein einfaches Wartezeitproblem bei einem Poissonschen Verkehrsfluss, österr. Ingr.-Arch., 16 (1): 75–90 (1961).MathSciNetMATHGoogle Scholar
  172. 172.
    Kremser, H., Ein zusammengesetztes Wartzeitproblem bei Poissonschen Verkehrsströmen, Osten. Ingr.-Arch., 16 (3): 231–252 (1962).Google Scholar
  173. 173.
    Lee, A. M., Some aspects of a control and communication system, Operat. Res. Quart., 10(4): 206–216 (1959)Google Scholar
  174. 174.
    Lee, A. M. and Longton, P. A., Queueing processes associated with airline passenger check-in, Operat. Res. Quart., 10 (1): 56–71 (1959).Google Scholar
  175. 175.
    Lee, G., A generalization of linear car-following theory, Operat. Res., 14 (4): 595–606 (1966).Google Scholar
  176. 176.
    Le Gall, P., Les trafics téléphoniques et la sélection conjuguée en téléphonie automatique, Ann. Telecommun., 13 (7–8): 186–207 (1958).Google Scholar
  177. 177.
    Le Gall, P., Les Systèmes avec ou sans Attente et les Processes Stochastiques, I: Généralités, Applications à la Recherche Opérationnelle, Dunod, Paris (1962), xiv + 482 pages.Google Scholar
  178. 178.
    Leroy, R. and Vaulot, A. E., Sur la proportion d’appels perdus dans certains systèmes, Compt. Rend., 220 (1): 84–85 (1945).MathSciNetMATHGoogle Scholar
  179. 179.
    Lewis, J. T. and Newell, G. F., Products of zero-one processes and the multilane highway crossing problem, J. Math. Anal. Appl., 16(1):51–64(1966).Google Scholar
  180. 180.
    Lighthill, M. J., The hydrodynamic analogy, Operas. Res. Quart., 8 (3): 109–114 (1957).Google Scholar
  181. 181.
    Mack, C., The efficiency of N machines unidirectionally patrolled by one operative when walking time is constant and repair times are variable, J. Roy. Statist. Soc., B19 (1): 173–178 (1957).MathSciNetMATHGoogle Scholar
  182. 182.
    Mack, C., Murphy, T. and Webb, N. L., The efficiency of N machines unidirectionally patrolled by one operative when walking time and repair times are constant, J. Roy. Statist. Soc., B19 (1): 166–172 (1957).MathSciNetMATHGoogle Scholar
  183. 183.
    Masterson, G. E. and Sherman, S., On queues in tandem, Ann. Math. Statist., 34 (1): 300–307 (1963).MathSciNetMATHCrossRefGoogle Scholar
  184. 184.
    May, A.D., Jr., and Keller, H. E. M., A deterministic queueing model, Transport. Res., 1 (2): 117–128 (1967).MATHGoogle Scholar
  185. 185.
    McMillan, B., A moving single server problem, Ann. Math. Statist., 28 (2): 471–478 (1957).MathSciNetMATHCrossRefGoogle Scholar
  186. 186.
    Meisling, T., Discrete-time queueing theory, Operas. Res., 6 (1): 96–105 (1958).MathSciNetGoogle Scholar
  187. 187.
    Meissl, P., Stochastisches Modell einer festzeitgesteuerten Rot-Grün-Signalanlage (I Teil), Z. Mod. Rechentech. Automat., 9 (1): 11–18 (1962).Google Scholar
  188. 188.
    Meyer, R. F. and Wolfe, H. B., The organization and operation of a taxi fleet, Naval Res. Logist. Quart., 8 (2): 137–150 (1961).MathSciNetMATHCrossRefGoogle Scholar
  189. 189.
    Miller, A. J., Road Traffic flow considered as a stochastic process, Proc. Cambridge Phil. Soc., 58 (2): 312–325 (1962).Google Scholar
  190. 190.
    Miller, R. G., Jr., Priority queues, Ann. Math. Statist., 31 (1): 86–103 (1960).MathSciNetMATHCrossRefGoogle Scholar
  191. 191.
    Mirasol, N. M., A queueing approach to logistics systems, Operat. Res., 12 (5): 707–724 (1964).Google Scholar
  192. 192.
    Moran, P. A. P., The Engset distribution in telephone congestion theory, Austral. J. Appl. Sci., 12(3):257–264(1961).Google Scholar
  193. 193.
    Myers, P. J., Monte Carlo: reliability tool for design engineers, Proc. Ninth Nat. Sympos. Reliability and Quality Control, San Fransisco, Calif., 1963, Inst. Radio Engrs., New York (1963), pp. 487–592.Google Scholar
  194. 194.
    Naor, P., On machine interference,J.Roy. Statist. Soc., B18(2):280–287(1956).Google Scholar
  195. 195.
    Naor, P., Normal approximation to machine interference with many repairments, J. Roy. Statist. Soc., B19 (2): 334–341 (1957).Google Scholar
  196. 196.
    Newell, D. J., Immediate admissions to hospitals, Actes 3–4 Conf. Internat. Rech., Operat., Oslo, 1963, Paris-London (1964), pp. 224–233.Google Scholar
  197. 197.
    Newell, G. F., Statistical analysis of the flow of highway traffic through a signalized intersection, Quart. Appl. Math., 13 (4): 359–369 (1956).MathSciNetGoogle Scholar
  198. 198.
    Newell, G. F., Queues for a fixed-cycle traffic light, Ann. Math. Statist., 31 (3): 589–597 (1960).MathSciNetCrossRefMATHGoogle Scholar
  199. 199.
    Oliver, R. M., A traffic-counting distribution, Operat. Res., 9 (6): 802–840 (1961).MathSciNetGoogle Scholar
  200. 200.
    Oliver, R. M., Distribution of gaps and blocks in a traffic stream, Operat. Res., 10 (2): 197–217 (1962).MathSciNetMATHGoogle Scholar
  201. 201.
    Oliver, R. M., Delays to aircraft serviced by the glide-path, Operat. Res. Quart., 13 (2): 201–209 (1962).Google Scholar
  202. 202.
    Oliver, R. M. and Bisbee, E. E., Queueing for gaps in high-flow traffic streams, Operat. Res., 10 (1): 105–144 (1962).MathSciNetMATHGoogle Scholar
  203. 203.
    Oliver, R. M. and Thibault, B., A high-flow traffic-counting distribution, Highway Res. Board Bull., No. 356, pp. 15–27 (1962).Google Scholar
  204. 204.
    Page, E. S., On Monte Carlo methods in congestion problems, I: Searching for an optimum in discrete situations, Operat. Res., 13 (2): 291–299 (1965).MathSciNetGoogle Scholar
  205. 205.
    Palm, C., Intensitàtsschwankungen in Fernsprechverkehr, Ericsson Tech., 44: 1189 (1943).MathSciNetMATHGoogle Scholar
  206. 206.
    Pearcey, T., Delays in landing of air traffic, J. Roy. Aeronaut. Soc., 52: 799–812 (1948).Google Scholar
  207. 207.
    Pestalozzi, G., Priority rules for runway use, Operat. Res., 12 (6): 941–950 (1964).Google Scholar
  208. 208.
    Petigny, B., Le calcul des probabilités et la circulation des véhicules, Ann. Ponts et Chaussees, 136 (2): 77–92 (1966).Google Scholar
  209. 209.
    Phipps, T. E., Machine repair as a priority waiting-line problem, Operat. Res., 4 (1): 76–86 (1956).Google Scholar
  210. 210.
    Pollaczek, F., Développement de la théorie stochastique des lignes téléphoniques pour un état initial quelconque, Compt. Rend., 239 (25): 1764–1766 (1954).MathSciNetMATHGoogle Scholar
  211. 211.
    Pollaczek, F., Problèmes stochastiques posés par le phénomène de formation d’une queue d’attente à un guichet et par des phénomènes apparentes, Mem. Sci. Math., No. 136, Gauthier-Villars, Paris (1957), 123 pages.Google Scholar
  212. 212.
    Pollaczek, F., Application de la théorie des probabilités à des problèmes posés par l’encombrement des réseaux téléphoniques, Ann. Telecommun., 14 (7–8): 165–183 (1959).MathSciNetGoogle Scholar
  213. 213.
    Pollaczek, F., Fonctions de répartition relatives a un groupe de lignes téléphoniques sans dispositif d’attente, Compt. Rend., 248 (3): 353–355 (1959).MathSciNetMATHGoogle Scholar
  214. 214.
    Pollaczek, F., Sur le calcul des probabilités des délais d’attente dans le cas d’un groupe des lignes téléphoniques, PTT -Bedrijf, 9 (4): 202–203 (1960).Google Scholar
  215. 215.
    Popp, W., Simulationstechnik bei Lagerplanung mit stochastischer Nachfrage Unternehmensforschung, 7 (2): 65–74 (1963).MathSciNetMATHGoogle Scholar
  216. 216.
    Potthoff, G.,Das Millen und Leeren von Gleisgruppen, Wiss. Z. Hochschule Verkehrswesen Dresden, 6(1):13–32 (1958–59).Google Scholar
  217. 217.
    Pritsker, A. and Alan B., Application of multichannel queueing results to the analysis of conveyor systems, J. Industr. Engng., 17 (1): 14–21 (1966).Google Scholar
  218. 218.
    Radström, H., Unformning avbusshallplaster, Medd. Forskarnas Kontaktorgan. IVA, No. 26, pp. 45–48 (1957).Google Scholar
  219. 219.
    Randazzo, F. P., Optimization of network configurations through queueing theory, Electr. Commun., 38 (4): 511–523 (1963).Google Scholar
  220. 220.
    Rényi, A., On two mathematical modesls of the traffic on a divided highway, J. Appl. Probabil., 1 (2): 311–320 (1964).MATHCrossRefGoogle Scholar
  221. 221.
    Riordan, J., Stochastic Service Systems, Wiley, New York (1962), 139 pages.Google Scholar
  222. 222.
    Rosenberg, M., The machine repair problem with ancillary work, Actes 3-e Conf. Internat. Rech. Operat., Oslo, 1963, Paris-London (1964), pp. 861–863Google Scholar
  223. 223.
    Rsoenshine, M., Queues with state-dependent service times, Transport. Res., 1 (2): 97–104 (1967).Google Scholar
  224. 224.
    Rothery, R., Silver, R., Herman, R. and Torner, C., Analysis of experiments on single-lane bus flow, Operat. Res., 12 (6): 913–933 (1964).MATHGoogle Scholar
  225. 225.
    Saaty, T. L., Elements of Queueing Theory with Applications, McGraw-Hill, New York (1961).MATHGoogle Scholar
  226. 226.
    Sandeman, P., Empirical design of priority waiting times for jobbing shop control, Operas. Res., 9 (4): 446–455 (1961).Google Scholar
  227. 227.
    Sarkadi, K., Mozdonyok varakozási idejeröl, A Magyar Tud, Akad. Alkalm. Mat. Int. Közl., 3(1–2):191–194 (1954–55).Google Scholar
  228. 228.
    Schuhl, A., La calcul des probabilités et la répartition des véhicules sur les routes à deux voies de circulation, Travaux, 39 (243): 16–18 (1955).Google Scholar
  229. 229.
    Schuhl, A., Hasard et probabilité dans les problèmes de circulation rout è.re, J. Soc. Statist. Paris, 97 (10–12): 233–251 (1956).Google Scholar
  230. 230.
    Schuhi, A., Stacking planes at LGA, Manag. Operat. Res. Digest, 1 (3): 7–9 (1956).Google Scholar
  231. 231.
    Steer, D. T. and Page, A., Feasibility financial studies of a port installation, Operat. Res. Quart., 12 (3) (1961).Google Scholar
  232. 232.
    Stephan, F. F., Two queues under preemptive priority with Poisson arrival and service rates, Operas. Res., 6 (3): 399–418 (1958).MathSciNetGoogle Scholar
  233. 233.
    Störmer,H.,über den zeitlichen Verlauf der Zustandswahrscheinlichkeiten in vollkommen Leitungsbündeln, Arch. Elektr. Übertrag., 12 (4): 173–176 (1958).Google Scholar
  234. 234.
    Störmer,H., Überein Warteproblem aus der Vermittlungstechnik, Z. Angew. Math, und Mech., 40 (5–6): 236–246 (1960).Google Scholar
  235. 235.
    Stover, A. M., Application of queueing theory to operation and expansion of a chemical plant, Chem. Engng. Progr. Sympos, Ser., 59 (42): 74–77 (1963).Google Scholar
  236. 236.
    Sugawara, S. and Takahashi, M. O., On some queues occurring in an integrated iron and steel works, J. Operat. Res. Soc. Japan, 8 (1): 16–23 (1965).MathSciNetMATHGoogle Scholar
  237. 237.
    Swersey, R. J., Closed networks of queues, Doct. Dissert., Univ. California, Berkeley (1966), 65 pages; Dissert. Abstr., B28 (1): 267 (1967).Google Scholar
  238. 238.
    Syski, R., Introduction to Congestion Theory in Telephone Systems, Oliver and Boyd, Ltd., Edinburgh-London (1960).Google Scholar
  239. 239.
    Takaacs, L., Eqy közlekedéssel kapcxolatos valószlnüségszámitási problémáról, Magyar Tud, Akad. Mat. Kutat6 Int. Käzl., 1 (1–2): 99–107 (1956).Google Scholar
  240. 240.
    Takács, L., On a stochastic process concerning some waiting -time problems, Teor. Veroyat. i Prim., 2 (1): 92–105 (1957).Google Scholar
  241. 241.
    Takács. L., On a combined waiting-time and loss problem concerning telephone traffic, Ann. Univ. Sci. Budapest., Sec. Math., 1: 73–82 (1958).MATHGoogle Scholar
  242. 242.
    Takács. L., A telefonforgalom elméletének néhany valószinüségaszámitási kérdéséröl, Magyar Rud. Akad. Mat. és Fiz. Tud. Oszt. közl., 8 (2): 151–210 (1958).Google Scholar
  243. 243.
    Takács, L., On the limiting distribution of the number of coincidences concerning telephone traffic, Ann. Math. Statist., 30 (1): 134–142 (1959).MathSciNetMATHCrossRefGoogle Scholar
  244. 244.
    Takács, L., Stochastic processes with balking in the theory of telephone traffic, Bell Syst. Tech. J., 40 (3): 795–820 (1961).Google Scholar
  245. 245.
    Takacs, L., The time dependence of Palm’s loss formula, J. Math. Anal. Appl., 2(1):58–71 (1961)Google Scholar
  246. 246.
    Takács, L., Priority queues, Operat. Res., 12(1): 63–74(1964).Google Scholar
  247. 247.
    Takacs, L., Two queues attended by a single server, Operat. Res., 16 (3): 639 650 (1968)Google Scholar
  248. 248.
    Tanner, J. C., A problem of interference between two queues, Part 1, Biometrika, 40 (2): 58–59 (1953).MathSciNetMATHGoogle Scholar
  249. 249.
    Tanner, J. C., A simplified model for delays in overtaking on a two-lane road, J. Roy. Statist. Soc., B20 (2): 408–414 (1958).MathSciNetMATHGoogle Scholar
  250. 250.
    Tanner, J. C., Delays on a two-lane road, J. Roy. Statist. Soc., B23 (1): 38–63 (1961).Google Scholar
  251. 251.
    Tanner, J. C., A derivation of the Borel distribution, Biometrika, 48 (1–2): 222–224 (1961).MathSciNetMATHGoogle Scholar
  252. 252.
    Tanner, J. C., The capacity of an uncontrolled intersection, Biometrika, 54(3–4):657–658(1967).Google Scholar
  253. 253.
    Thedeen, T., A note on the Poisson tendency in traffic distributions, Ann. Math. Statist., 35 (4): 1823–1824 (1964).MathSciNetMATHCrossRefGoogle Scholar
  254. 254.
    Thurmann, W. H., Wahrscheinlichkeitstheoretische Grundlagen bei mehrstelliger Gruppenarbeit, Teil 1, Automatik, 7 (1): 30–34 (1962).Google Scholar
  255. 255.
    Toft, F. J. and Boothroyd, H., A queueing model for spare coal faces, Operat. Res. Quart. 10 (4): 245–251 (1959).Google Scholar
  256. 256.
    Kanehisa, Udagawa and Gisaku, Nakamura, On a queue in which joining customers give up their services half way, J. Operat. Res. Soc. Japan, 1 (2): 59–76 (1957).Google Scholar
  257. 257.
    Van Slyke, R. M., Monte Carlo methods and the PERT problem, Operat. Res., 11 (5): 839–860 (1963).Google Scholar
  258. 258.
    Van Voorhis, W. R., Waiting-line theory as a management tool, Operat. Res., 4 (2): 221–231 (1956).Google Scholar
  259. 259.
    Vaulot, A. E., Extension des formules d’Erlang au cas ou les durées des conversations suivent une loi quelconque, Rev. Gen. Elec., 22: 1164–1171 (1927).Google Scholar
  260. 260.
    Ventura, E., Application de la théorie des files d’attente a la détermination des installations de chargement et de l’horaire de travail optima pour un port à quai minéralier unique, Rev. Rech. Operat., 2 (6): 48–58 (1958).Google Scholar
  261. 261.
    Wallström, B., Alternative routing in a two-stage link system; congestion theory and simulated traffic studies, Ericsson Tech., 17 (2): 261–285 (1961).Google Scholar
  262. 262.
    Weiss, G. H., An analysis of pedestrian queueing, J. Res. Nat. Bur. Stds., B67 (4): 229–243 (1963).MATHGoogle Scholar
  263. 263.
    Weiss, G. H., Effects of a distribution of gap acceptance functions on pedestrian queues, J. Res. Nat. Bur. Stds., B68 (1): 31–33 (1964).MATHGoogle Scholar
  264. 264.
    Weiss, G. H., The intersection delay problem with gap acceptance function depending on speed and time, Transport. Res., 1 (4): 367–371 (1967).Google Scholar
  265. 265.
    Weiss, G. H. and Herman, R., Statistical properties of low-density traffic, Quart. Appl. Math., 20 (2): 121–130 (1962).MathSciNetMATHGoogle Scholar
  266. 266.
    Weiss, G. H. and Maradudin, A. A., Some problems in traffic delay, Operat. Res., 10 (1): 74–104 (1962).Google Scholar
  267. 267.
    White, H. and Christie, L. S., Queueing with preemptive priorities or with breakdown, Operas. Res., 6 (1): 79–95 (1958).MathSciNetGoogle Scholar
  268. 268.
    Wilkinson, R. I., The interconnection of telephone systems -graded multiples, Bell Syst. Tech. J., 10: 531–564 (1931).Google Scholar
  269. 269.
    Yadin, M. and Naor, P., Queueing systems with a removable service station, Operat. Res. Quart., 14 (4): 393–405 (1963).Google Scholar
  270. 270.
    Yeo, G. F., Traffic delays on a two-lane road, Biometrika, 51 (1–2): 11–15 (1964).MathSciNetMATHGoogle Scholar
  271. 271.
    Yeo, G. F. and Weesakul, B., Delays to road traffic at an intersection, J. Appl, Probabil., 1(2): 29’7–310 (1964).Google Scholar
  272. 272.
    Yokota, H., Analysis of the capacity of arrival lines in the hump yard, Rep. Statist. Appl. Res. Union Japan. Scientists and Engrs., 11 (1): 36–46 (1964).Google Scholar
  273. 273.
    Zitek,F., Príspevek k theorii smisenych systémn hromadné obsluhy, Aplikace Mat., 2 (2): 154–159 (1967).Google Scholar

Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • N. P. Buslenko
  • A. P. Cherenkov

There are no affiliations available

Personalised recommendations