Performance Analysis of a Markovian Queue with Impatient Customers and Working Vacation

doi:10.1007/s40305-021-00361-w

Abstract

Abstract: In this paper, we consider the impatient customers in M/M/1 queueing model under variant working vacation policy. The customer's impatience is due to its arrival during a working vacation period, where the service rate of the customer is lower than a normal busy period. If the system is non-empty when the server returns from the working vacation, the server resumes the normal service period. Otherwise, the server will take successive working vacations till it reaches the maximum number of K working vacations and then the server remains idle until the next arrival. Closed-form probabilities are obtained by using the identities involving beta functions and degenerate hypergeometric functions, and the performance measures of the system are derived using generating functions. The stochastic decomposition structures of the mean queue length and mean waiting time are verified. The effects of the system parameters on some performance measures had been numerically illustrated.

Key words: Markovian queue, Variant working vacations, Probability generating function

CLC Number:

Shakir Majid. Performance Analysis of a Markovian Queue with Impatient Customers and Working Vacation[J]. Journal of the Operations Research Society of China, 2023, 11(1): 133-156.

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