On a queuelng process with arrival and service rates depending on the number of units served

摘要

A queueing problem in which arrival rate and service rate depending on the number of units served is considered. Considerwhere X(t) is the number of units in the system at time t and Y(t) is the number of units served upto that time. Clearlyis a bivariate MARKOV Process. Explicit expression foris obtained whenmassumes the value 0 or 1, and. Various other quantities of interest are also computed. An optimization problem related to this model is considered.