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Unreliable multiserver queueing system with modified vacation policy. (English) Zbl 1397.90105
Summary: This paper presents modeling and analysis of Markovian multiserver queue under (\(e, d\)) single vacation policy with server breakdowns and repairs. In such a system with \(c\) servers, when some (say \(d < c\)) servers become idle at a service completion time, then \(e(\leq d)\) servers take single vacation only. During idle as well as busy state, the servers are subject to accidental breakdowns. We formulate the model as a quasi-birth-and-death (QBD) process. By employing matrix geometric method, some stationary performance measures after service completion are established. Furthermore, the direct search algorithm is used to simultaneously determine the optimal number of idle, vacationing and total number of servers at minimum cost. Numerical illustration is facilitated to explore the effect of the number of servers, vacation rate, failure and repair rates on the performance measures of interest. Furthermore, the numerical results obtained are compared by using soft computing approach based on adaptive neuro fuzzy inference system (ANFIS).
MSC:
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
Software:
MOSEL
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