Dynamic Routing in a Queueing System with a Multiple Service Facility

In this paper we analyze a problem of traffic assignment within a queueing system with multiple service facilities subject to a changing load. The evolution in time of the mean number in the system is approximated with a nonlinear differential equation. The dynamic flow pattern is found for which the total waiting time of all entities passing the system is minimal. A numerical example is given. For the system in a nonstationary environment an adaptive strategy developed in this paper is compared with the performance of the policy of joining the shorter queue.