On bounds of response time performance achievable by multiclass single- server queues (Q1338906)

Multiclass M/G/1 systems in steady-state with work-conserving scheduling strategies are studied. Restricting a system's scheduling strategy to making no direct use of the required service times, every time the server becomes idle its memory is cleared, and service may only be interrupted by newly arriving customers, a conservation law is developed by means of inequalities. The conservation law states that if a response time vector composed of the expected response times of the different classes of a system in steady-state is achievable, then it must belong to a well- defined convex polytope (a set bounded by hyperplanes). Furthermore, on each hyperplane bounding the relevant polytope there lies at least one vertex of the convex set of achievable response time vectors. Therefore, this polytope is the least one including the set of all achievable response time vectors.