The goal of this paper is to assess the improvement in performance that might be achieved by optimally scheduling a multiclass open queueing network. A stochastic process is defined whose steady-state mean value is less than or equal to the mean number of customers in a queueing network under any arbitrary scheduling policy. Thus, this process offers a lower bound on performance when the objective of the queueing network scheduling problem is to minimize the mean number of customers in the network. Since this bound is easily obtained from a computer simulation model of a queueing network, its main use is to aid job-shop schedulers in determining how much further improvement (relative to their proposed policies) might be achievable from scheduling. Through computational examples, we identify some factors that affect the tightness of the bound.
"Performance Bounds for Scheduling Queueing Networks." Ann. Appl. Probab. 2 (2) 460 - 480, May, 1992. https://doi.org/10.1214/aoap/1177005711