## Service station factors in monotonicity of retrial queues.(English)Zbl 1042.60544

Summary: A retrial queue consists of an orbit with infinite capacity, a service station, and a queue with finite capacity $$B$$. If any customer attempting the queue is blocked due to saturation, he then enters the orbit where the customer waits for some time, called retrial time, before the next retrial attempt. We show that if the hazard rate function of the retrial time distribution is decreasing, then stochastically longer service time or less servers will result in more customers in the system.

### MSC:

 60K25 Queueing theory (aspects of probability theory) 90B22 Queues and service in operations research
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### References:

 [1] Yang, T.; Templeton, J.G.C., A survey on retrial queues, Questa, 2, 201-233, (1987) · Zbl 0658.60124 [2] Falin, G.I., A survey of retrial queues, Questa, 7, 127-168, (1990) · Zbl 0709.60097 [3] Kulkarni, V.G.; Liang, H.M., Retrial queues revisited, (), 19-34 · Zbl 0871.60074 [4] Liang, H.M.; Kulkarni, V.G., Monotonicity properties of single-server retrial queues, Stochastic models, 9, 373-400, (1993) · Zbl 0777.60091 [5] Khalil, Z.; Falin, G., Stochastic inequalities for M/G/1 retrial queues, Operations research letters, 16, 285-290, (1994) · Zbl 0819.60090 [6] Liang, H.M.; Kulkarni, V.G., Stability condition for a single-server retrial, Adv. appl. prob., 25, 690-701, (1993) · Zbl 0781.60093 [7] Kamae, T.; Krengel, U.; O’Brien, G., Stochastic inequalities on partially ordered spaces, Ann. prob., 5, 899-912, (1977) · Zbl 0371.60013
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