Authors: K. Rasmi; M.J. Jacob
Addresses: Department of Mathematics, National Institute of Technology Calicut, Kerala, Calicut – 673601, India ' Department of Mathematics, National Institute of Technology Calicut, Kerala, Calicut – 673601, India
Abstract: This paper considers a Markovian queueing inventory system with c servers and optional self-service facility, driven by an inventory under the (s, S) protocol. When an arrival occurs, if both an idle server and free inventory are available, then service by a server is initiated. If a customer on arrival finds all servers active but free inventory available, then he can either wait for the server (join the waiting line) or go for a self-service. A modified case of the framework has been analysed by changing the presumption that in the event when an arriving customer finds all the servers active, but a few inventories free will choose to have self-service. Here also we obtain steady-state probabilities and express a cost function in terms of some important performance measures. We made a point to point investigation on recycle time. A cost optimisation problem has been stated and numerically solved. Also, the impacts of certain parameters on a few performance measures are moreover outlined numerically.
Keywords: multiserver queue; self-service; (s, S) inventory; matrix analytic method.
International Journal of Mathematical Modelling and Numerical Optimisation, 2021 Vol.11 No.3, pp.275 - 291
Received: 04 Aug 2020
Accepted: 25 Aug 2020
Published online: 29 Jul 2021 *