A queueing system with returning customers and waiting line. (English) Zbl 0836.90072
Summary: We consider a queueing system where a customer who finds all channels busy must decide either to join the queue or to retry after an exponentially distributed time. The performance of the system can be approximated by using the RTA approximation introduced by Wolff and Greenberg. We present numerical results demonstrating the performance of the approximation for various representative cases.
MSC:
| 90B22 | Queues and service in operations research |
| 60K25 | Queueing theory (aspects of probability theory) |
References:
| [1] | Artalejo, J. R., Explicit formulae for the characteristics of the M/\(H_2/1\) retrial queue, J. Oper. Res. Soc., 44, 309-313 (1993) · Zbl 0771.60073 |
| [2] | Deul, N., Stationary conditions for multiserver queueing systems with repeated calls, Elektron. Informationsverarbeitung Kybern., 16, 607-613 (1980) · Zbl 0476.90027 |
| [3] | Falin, G. I., On sufficient conditions for ergodicity of multichannel queueing systems with repeated calls, Adv. Appl. Probab., 16, 447-448 (1984) · Zbl 0535.60087 |
| [4] | Falin, G. I., A survey of retrial queues, Queueing Systems, 7, 127-167 (1990) · Zbl 0709.60097 |
| [5] | Greenberg, B. S., M/G/1 queueing systems with returning customers, J. Appl. Probab., 26, 152-163 (1989) · Zbl 0672.60094 |
| [6] | Greenberg, B. S.; Wolff, R. W., An upper bound on the performance of queues with returning customers, J. Appl. Probab., 24, 466-475 (1987) · Zbl 0626.60092 |
| [7] | Jacobson, N., Basic Algebra I (1985), Freeman: Freeman New York · Zbl 0557.16001 |
| [8] | Neuts, M. F.; Rao, B. M., Numerical investigation of a multiserver retrial model, Queueing Systems, 7, 169-190 (1990) · Zbl 0711.60094 |
| [9] | Pearce, C. E.M., Extended continued fractions, recurrence relations and two-dimensional Markov processes, Adv. Appl. Probab., 21, 357-375 (1989) · Zbl 0672.60073 |
| [10] | Tweedie, R. L., Sufficient conditions for regularity, recurrence and ergodicity of Markov processes, (Math. Proc. Cambridge Philos. Soc., 78 (1975)), 125-136 · Zbl 0331.60047 |
| [11] | Wolff, R. W., Stochastic Modeling and the Theory of Queues (1989), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0701.60083 |
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