Systematic analysis of an unreliable batch service retrial queueing system with two sort of vacation
by S.P. Niranjan; K. Indhira; V.M. Chandrasekaran
International Journal of Applied Systemic Studies (IJASS), Vol. 10, No. 3, 2023

Abstract: This paper concentrates on bulk arrival and batch service retrial queueing system with server failure, two types of vacation and constant retrial rate. If an arrival of customers finds a server is free then batch service will be provided with minimum of one customers and maximum of 'b' customers. On the contrary, if the arrival of customers finds the server is busy then entire customers will join in the orbit to explore service again. After service completion, if there are no customers in the orbit then the server leaves for working vacation. During working vacation, the server provides service in lower service rate compared to regular service rate. In the working vacation completion, if the orbit size is zero then the server leaves for non-working vacation. The server may get failure in working period. If the server got failure with probability (φ) then the renewal of service station will be considered. On the other hand, if there is no breakdown and orbit is empty then the server leaves for working vacation with probability (1 - φ). For this designed queueing model probability generating function of the orbit size will be obtained. Various performance measures are also be derived with suitable numerical illustrations.

Online publication date: Thu, 19-Oct-2023

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