## An $$M/G/1$$ retrial queue with unreliable server for streaming multimedia applications.(English)Zbl 1178.60066

Summary: As a model for streaming multimedia applications, we study an unreliable retrial queue with infinite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable. Customers join the retrial orbit if and only if their service is interrupted by a server failure. Interrupted customers do not rejoin the normal queue but repeatedly attempt to access the server at independent and identically distributed intervals until it is found functioning and idle. We provide stability conditions, queue length distributions, stochastic decomposition results, and performance measures. The joint optimization of the retrial and server repair rates is also studied.

### MSC:

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

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