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Confidence interval for M/M/2 queue with heterogeneous servers. (English) Zbl 0723.60115
The authors use the results of U. Dave and Y. K. Shah [J. Oper. Res. Soc. 31, 423-426 (1980; Zbl 0447.62078)]. Dave and Shah estimated the arrivals and service rates based on maximum likelihood principles assuming the queue in equilibrium. In this paper, H. W. Lilliefors’technique [Oper. Res. 14, 723-727 (1966)] is employed to derive the confidence intervals for the parameters of M/M/2 queue with heterogeneous servers. In this queueing system, customers wait in line according to their arrival. When both servers are idle, the faster server is scheduled for service before the slower one. The average number of customers N in the system is given by K. S. Trivedi [Probability and statistics with reliability, queueing, and computer science applications (1982; Zbl 0513.60001, Zbl 0513.60002)] and in another form by the authors of this note.

MSC:
60K25 Queueing theory (aspects of probability theory)
62M99 Inference from stochastic processes
90B22 Queues and service in operations research
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References:
[1] Clarke, A.B., Maximum likelihood estimates in a simple queue, Ann. math. statist., 28, 1036-1040, (1957) · Zbl 0078.33602
[2] Dave, U.; Shah, Y.K., Maximum likelihood estimates in M/M/2 queue with heterogeneous servers, J. oper. res. soc., 31, 423-426, (1980) · Zbl 0447.62078
[3] Gross, D.; Harris, C.M., Fundamentals of queueing theory, (1985), Wiley New York · Zbl 0658.60122
[4] Lilliefors, H.W., Some confidence interval for queues, Oper. res., 14, 723-727, (1966)
[5] Trivedi, K.S., Probability and statistics with reliability, queueing and computer science applications, (1982), Prentice-Hall Englewood Cliffs, NJ
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