Bounding the Performance of BCMP Networks with Load-Dependent Stations

In this paper, we introduce new bounds on the system throughput and response time of closed, single-class BCMP queueing networks with load-dependent stations. Under the assumption that stations relative service rates are non-decreasing functions of their queue lengths, the bounds derive from the monotonicity of system throughput and queue-lengths and exploit the asymptotic equivalence that exists between closed and open single-class BCMP networks when the number of jobs N populating a closed network grows to infinity. The bounds can be applied when N is sufficiently large and the minimum N which allows their use is given. Experimental results present scenarios in which the proposed bounds significantly improve the accuracy of existing techniques and we analytically show that they are always more accurate than the popular balanced job bounds when N is greater than a given threshold.