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On multiserver feedback retrial queues with balking and control retrial rate. (English) Zbl 1102.60079
The paper considers a multiserver retrial queueing system in which primary customers arrive according to a Poisson process. The service facility consists of a finite number of identical servers and service times are exponentially distributed. An arriving customer who finds all servers busy enters the retrial group with probability $p$ or is lost forever with probability $1 - p$. If the primary customer finds some servers free, he immediately occupies a server and obtains service. After the customer is served completely, he decides either to join the retrial group again for another service with probability $1 - \theta $ or to leave the system forever with probability $\theta $. Every customer in the retrial group conducts a retrial after an exponentially distributed amount of time and is independent of the number of customers applying for service. Upon return from the retrial group, customers who find all servers busy always rejoin the retrial group; this operation continues until they are eventually served. The probability of a repeated attempt during $(t,t + dt)$, given that $n$ customers are in orbit at time $t$, is $n\sigma dt + o(dt)$. This system is analyzed as a quasi-birth-and-death process and a necessary and sufficient condition for stability of the system is discussed. The effects of various parameters on the system performance measures are illustrated numerically. Finally, the optimization of the retrial rate and specific probabilistic descriptors of the system are investigated.

60K25Queueing theory
90B22Queues and service (optimization)
Full Text: DOI
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