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M/M/c/K loss and delay interdependent queueing model with controllable arrival rates and no passing

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Abstract

In this paper a finite capacity, loss and delay, interdependent queueing system with controllable arrival rates and no passing has been considered. For this model, the steady state probabilities are derived and the average waiting times for the two types of customers (elective and emergency) are obtained for varying arrival rates when the arrival and service processes are interdependent. Numerical examples are given for a better understanding.

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References

  • Aftab Begum, M.I., and D. Maheswari. 2002. The M/M/c/ ∞ interdependent queueing model with controllable arrival rates. Opsearch 39(2):89–110.

    MathSciNet  MATH  Google Scholar 

  • Bhat, U.N. 1969. Queueing system with first order dependence. Opsearch 6:1–24.

    MathSciNet  Google Scholar 

  • Borst, S.C., and M.B. Combe. 1992. Letters to the Editors:Busy period analysis of correlated queues. Journal of Applied Probability 29:482–483.

    Article  MathSciNet  Google Scholar 

  • Boxma, O.J. 1984. The joint arrival and departure process for the M/M/1 queue. Statistica Neerlandica, 38:199–208.

    Article  MathSciNet  MATH  Google Scholar 

  • Conolly, B.W. 1968. The waitig time process for a certain correlated queue. Operational Research 16:1006–1015.

    MATH  Google Scholar 

  • Conolly, B.W., and Q.H. Choo. 1979. The waitig time process for a generalised corrrelated queue with exponential demand and service. SIAM Journal on Applied Mathematics 37:263–275.

    Article  MathSciNet  MATH  Google Scholar 

  • Conolly, B.W., and N. Hadidi. 1969. A correlated queue. Journal of Applied Probability 6:122–136.

    Article  MathSciNet  MATH  Google Scholar 

  • Jain, M. 1998. Finite population loss and delay queueing system with no passing. Opsearch 35(3):261–276.

    MathSciNet  MATH  Google Scholar 

  • Langaris, C. 1987. Busy period analysis of a correlated queue. Journal of Applied Probability 24:476–485.

    Article  MathSciNet  MATH  Google Scholar 

  • Mitchell, C.R., and A.S. Paulson. 1979. M/M/1 queues with interdependent arrival and service process. Naval Research Logistics Quarterly 26:47–56.

    Article  MATH  Google Scholar 

  • Sharma, M.B., and G.C. Kumar. 1983. A limited mnlti server queue without passing. Indian Journal of Pure and Applied Mathematics 14(8):935–939.

    MATH  Google Scholar 

  • Srinivasa Rao, K., Shobha, T., and P. Srinivasa Rao. 2000. The M/M/1/ ∞ interdependent queueing model with controllable arrival rates. Opsearch 37(1):14–24.

    MathSciNet  MATH  Google Scholar 

  • Srinivasan, A., and M. Thiagarajan. 2006a. The M/M/1/K interdependent queueing model with controllable arrival rates. International Journal of Management and Systems 22(1):23–34.

    Google Scholar 

  • Srinivasan, A., and M. Thiagarajan. 2006b. The M [x]/M/1/ ∞ interdependent queueing model with controllable arrival rates. Journal of Decision And Mathematical Sciences 11(1–3):7–24.

    Google Scholar 

  • Srinivasan, A., and M. Thiagarajan. 2007a. A finite capacity multi server Poisson input queue with interdependent inter-arrival and service times and controllable arrival rates. Bulletin of Calcutta Mathematical Society 99(2):173–182.

    MathSciNet  Google Scholar 

  • Srinivasan, A., and M. Thiagarajan. 2007b. The M/M/c/K/N interdependent queueing model with controllable arrival rates bulking,reneging and spares. Journal of Statistics and Applications 2(1–2):56–65.

    Google Scholar 

  • Srinivasan, A., and M. Thiagarajan. 2007c. Busy period analysis of M/M/1/ ∞ interdependent queueing model with controllable arrival rates. Acta Ciencia Indica XXXIIIM(1):19–24.

    MathSciNet  Google Scholar 

  • Srinivasan, A., and M. Thiagarajan. 2009. A finite population loss and delay queueing system with interdependent inter-arrival and service times,controllable arrival rates and no passing. Journal of Applied Statistical Science 17(1):47–64.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, St. Joseph’s College (Autonomous), Tiruchirappalli-620 002, Tamil Nadu, India

    M. Thiagarajan

  2. P.G and Research Department of Mathematics, Bishop Heber College, Tiruchirappalli, Tamil Nadu, India

    A. Srinivasan

Authors
  1. M. Thiagarajan
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  2. A. Srinivasan
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Correspondence to M. Thiagarajan.

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Thiagarajan, M., Srinivasan, A. M/M/c/K loss and delay interdependent queueing model with controllable arrival rates and no passing. Sankhya B 73, 316–330 (2011). https://doi.org/10.1007/s13571-011-0027-7

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  • DOI: https://doi.org/10.1007/s13571-011-0027-7

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