Efficient Heuristics for the Simulation of Buffer Overflow in Series and Parallel Queueing Networks

Many of recent studies have proved the tail equivalence result for Egalitarian Processor Sharing system: [EQUATION], where B (resp. V) is service requirement (resp. sojourn time) of a customer; for PS, g = 1 - ρ. In this paper, we consider time-shared systems in which the server capacity is shared by existing customers in proportion to (dynamic) weights assigned to customers. We consider two systems, 1) in which the weight of a customer depends on it Age (attained service), and 2) in which the weight depends on the residual processing time (RPT). We allow for a parameterized family of weight functions such that the weight associated with a customer that has received a service (or, has a RPT) of x units is ω(x) = xα for some -∞ < α < ∞. We then study the sojourn time of a customer under such scheduling discipline and provide conditions on α for tail equivalence to hold true, and also give the value of g as a function of α

Extension of heuristics for simulating population overflow in Jackson tandem queuing networks to non-Markovian tandem queuing networks

In this paper we extend previously proposed state-dependent importance sampling heuristics for simulation of population overflow in Markovian tandem queuing networks to non-Markovian tandem networks, and experimentally demonstrate the asymptotic efficiency of the resulting heuristics