Application of nonparametric laws in queueing systems and renewal theory. (Application des lois non paramétriques dans les systèmes d’attente et la théorie de renouvellement.) (French. English summary) Zbl 1057.62087
The authors propose a bounding methodology which combines the moment bounds of D. Sengupta [J. Appl. Probab. 31, 777–787 (1994; Zbl 0815.62071)] for the survival function of distributions of certain types with suitable comparison results for queueing and reliability models. In this way, upper and lower bounds are obtained for the stationary mean waiting time in the system GI/GI/1 if the interarrival-time distribution is IFR or NBU, as well as for the mean life time of a system consisting of two repairable components with exponential life times if the repair-time distribution is IFR, DFR, NBU or NWU.
Reviewer: Erik A. van Doorn (Enschede)
MSC:
| 62N05 | Reliability and life testing |
| 60K25 | Queueing theory (aspects of probability theory) |
| 60E15 | Inequalities; stochastic orderings |
| 60K05 | Renewal theory |
| 62G99 | Nonparametric inference |
| 90B22 | Queues and service in operations research |
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
Citations:
Zbl 0815.62071References:
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