Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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The Analysis of the M/M/1 Queue with Impatient Customers

  • Published : 2000.08.01
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Abstract

The M/M/1 queue with impatient customers is studied. Impatient customers wait for service only for limited time K/0 and leave the system if their services do not start during that time. Notice that in the analysis of virtual waiting time, the impatient customer can be considered as the customer who enters the system only when his/her waiting time does not exceed K. In this paper, we apply martingale methods to the virtual waiting time and obtain the expected period from origin to the point where the virtual waiting time crosses over K or reaches 0, and the variance of this period. With this results, we obtain the expected busy period of the queue, the distribution, expectation and variance of the number of times the virtual waiting time exceeding level K during a busy period, and the probability of there being no impatient customers in a busy period.

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References

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  2. Journal of Applied Probability v.22 A queueing system with impatient customers De Kok, A.G.;Tijms, H.C.
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  5. Annals of Probability v.11 Calculation of the Laplace transform of the length of the busy period for the M/G/1 queue via martingales Rosenkranz W.A.