Sharper light-traffic bounds for general MAMS queues

Develop more precise bounds on the mean queue length E[Q] for the general Markovian Arrivals and Markovian Service (MAMS) single-server queue, in which the arrival and completion rates are each modulated by independent finite-state continuous-time Markov chains, specifically in the light-traffic regime (small load ρ). The objective is to obtain sharper bounds than those currently available, which are tight in heavy traffic but can be loose at low ρ and slow switching rates.

Background

The paper derives explicit bounds for mean queue length in the general MAMS model that are tight in heavy traffic. Simulations confirm tightness near ρ → 1 and demonstrate strong performance for two-level systems across regimes.

For general MAMS systems, the authors observe that their bounds may be loose in light traffic, especially for slow switching. They explicitly state that obtaining more precise bounds for light traffic remains to be done.