Asian Research Journal of Mathematics

This paper analyzes an infinite-server queueing model with consultation by a consultant. The consultant does not directly serve customers, but instead provides consultation to the servers. The arrivals to the system and requirement of consultation follow independent Poisson processes. The service times at the servers are assumed to follow mutually independent and identically distributed exponential random variables. The duration of consultation is an exponentially distributed random variable. Using Neuts Rao’s truncation method, we derive explicit expression for the stability of the system with a sufficiently large level N and an appropriate truncation error ϵ. A special case of the model corresponding to zero consultation rate is considered, and it is shown that the system reduces to the classical M/M/∞ queueing model. Several important performance measures are analyzed numerically, followed by graphical illustrations and a sensitivity analysis of the system parameters.