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The service system \(M/M^ R/\infty\) with impatient customers. (English) Zbl 0656.60097

An infinite server system providing both individual service and batch service is studied. Any customer arriving in this system will decide whether or not to wait for batch service (which is more economical), depending on the number of customers already waiting for service before the arrival. If he decides to wait for batch service, a customer will not be served until a group of R customers has accumulated in the waiting line. Otherwise, the customer receives individual service immediately.
For this queueing system, the size distribution, the waiting time and some numerical aspects are presented.
Reviewer: A.Dvurečenskij

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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References:

[1] D.F. Holman, M.L. Chaudhry and B.R.K. Kashyap, On the number in the system GI X /M/?, Sankhy? 44 (1982), Ser. A Pt. 1, 294.
[2] D.F. Holman, M.L. Chaudhry and B.R.K. Kashyap, On the service system M X /G/?, Eur. J. Opl. Res. 13 (1983) 142. · Zbl 0507.90036 · doi:10.1016/0377-2217(83)90075-9
[3] L. Takács, On a coincidence problem concerning telephone traffic, Acta Math. Sci. Hungarica 9 (1958) 45. · Zbl 0085.12603 · doi:10.1007/BF02023865
[4] L. Takács,Introduction to the Theory of Queues (Oxford University Press, New York, 1962).
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