, Volume 11, Issue 1, pp 157–167 | Cite as

Queues with hyper-poisson arrivals and bulk exponential service

  • J. K. Goyal


In this paper the time-dependent solution of a queueing system is discussed under the conditions (i) the units arrive according to Hyper-Poisson distribution withl branches (ii) the queue-discipline is ‘first come first served’ (iii) the Service-time distribution is exponential with maximum capacity ofM units being served at one instant. Some results have been obtained when the waiting space is finite; in particular the probability for service to be idle has been obtained. Also for infinite queueing-space case, the expressions for the state probabilities and the mean queuelength under steady state conditions have been found.


Unit Circle State Probability Service Facility Service Pattern Generate Function Technique 
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.


  1. [1]
    Morse, P. M.: Queues, Inventories and Maintenance, Wiley, New York (1958).Google Scholar
  2. [2]
    Gupta S. K. andJ. K. Goyal: Queues with Hyper-Poisson Input and Exponential Output with Finite Waiting Space, Opns. Res. Vol. 12, No. 1, pp. 82–88 (1964).zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Bailey, N. T. J.: On Queueing Process with Bulk Service, J. Roy. Stat. B. 16, pp. 80–87 (1954).zbMATHMathSciNetGoogle Scholar
  4. [4]
    Miller, R. G.: A Contribution to the Theory of Bulk Queues, J. Roy. Stat. Soc. B. 21, pp. 320–337 (1959).zbMATHGoogle Scholar
  5. [5]
    Downton, F.: Waiting Time in Bulk Service Queues, J. Roy. Stat. Soc. B. 17, pp. 256–261 (1955).zbMATHMathSciNetGoogle Scholar
  6. [6]
    Keilson, J.: A general Bulk Queue as a Hilbert Problem, J. Roy. Stat. Soc. B. 24, pp. 344–358 (1962).zbMATHMathSciNetGoogle Scholar
  7. [7]
    Jaiswal, N. K.: A Bulk Service Queueing Problem with Variable Capacity, J. Roy. Stat. Soc. B. 23, pp. 143–148 (1961).zbMATHMathSciNetGoogle Scholar
  8. [8]
    Bailey, N. T. J.: A continuous Time Treatment of a Simple Queue Using Generating Functions, J. Roy. Stat. Soc. B. 16, pp. 288–291 (1954).zbMATHMathSciNetGoogle Scholar

Copyright information

© Physica-Verlag 1967

Authors and Affiliations

  • J. K. Goyal
    • 1
  1. 1.Department of MathematicsChrist Church CollegeKanpurIndia

Personalised recommendations