An Infinite Server Queue with Bulk Arrival and Catastrophes

Abstract

We deal with the infinite-server queue in which customer arrive ingroup of random size and are served singly.Customers are served as soon as they enter the queuing system till the catastrophe occurs. Catastrophe clears the system instantaneously and thisprocess is repeated periodically.After each catastrophe, the system takes some set-uptimebefore starting the service again.Renewal theory is used to derive the transient and steady stateprobabilitiesfor the number of customers in the system at any random epoch. The average number of customers cleared per unit time isalso found in steady state. Thistype of queuing systems is applicable to computer communication networks, transport networks, pest control and medical fields to mention a few.