Int. J. of Industrial and Systems Engineering   »   2008 Vol.3, No.6



Title: Steady state analysis of a Mx/G/1 queue with two service modes and multiple vacations


Author: S. Jeyakumar, R. Arumuganathan


Department of Mathematics, Chikkanna Government Arts College, Tirupur, Tamil Nadu 641 602, India.
Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore, Tamil Nadu 641 004, India


Abstract: This paper deals with a single server Poisson queue with state dependent service. The service is rendered with different service modes as singly or in bulk according to the queue length. The service starts only if at least one customer is waiting for service. The server switches over from single service to bulk service only at service initiation epoch according to the queue length. If the number of customers waiting for service is ξ (1 ≤ ξ < a), then the server serves one by one. At the service initiation epoch, if the number of waiting customers ξ is at least 'a' (a < b), then the service is rendered according to Neut's general bulk service rule. At the service completion epoch, if there are no customers in the queue, the server avails multiple vacations, until he finds at least one customer in the queue. The Probability Generating Function (PGF) of the queue size and performance measures are obtained. Numerical results are presented in order to illustrate the effectiveness of performance of the state dependent queue.


Keywords: bulk arrival; single service; batch service; supplementary variables; multiple vacations; single server Poisson queue; state dependent service; queue size; performance measures.


DOI: 10.1504/IJISE.2008.020681


Int. J. of Industrial and Systems Engineering, 2008 Vol.3, No.6, pp.692 - 710


Available online: 10 Oct 2008



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