Optimal scheduling in a multiserver stochastic network

Abstract

We consider a fundamental scheduling problem in a multiserver stochastic network consisting of 2 classes of customers and 2 classes of servers. Customers of class k arrive to queue k according to a Poisson process with rate λ k , k = 1, 2. The service times of class k customers at class ℓ servers are i.i.d. following an exponential distribution with mean μ k ℓ -1 , ∀ k , ℓ = 1, 2, where 0 < μ 11 , μ 12 , μ 22 < ∞ and μ 21 = 0. Hence, class 1 customers can be served at both classes of servers, but class 2 customers can only be served at class 2 servers. A FCFS queueing discipline is employed at each queue. The customer arrival and service processes are mutually independent of each other and of all resource allocation decisions.