Analysis of Markovian Arrivals and Service with Applications to Intermittent Overload

Almost all queueing analysis assumes i.i.d. arrivals and service. In reality, arrival and service rates fluctuate over time. In particular, it is common for real systems to intermittently experience overload, where the arrival rate temporarily exceeds the service rate, which an i.i.d. model cannot capture. We consider the MAMS system, where the arrival and service rates each vary according to an arbitrary finite-state Markov chain, allowing intermittent overload to be modeled. We derive the first explicit characterization of mean queue length in the MAMS system, with explicit bounds for all arrival and service chains at all loads. Our bounds are tight in heavy traffic. We prove even stronger bounds for the important special case of two-level arrivals with intermittent overload. Our key contribution is an extension to the drift method, based on the novel concepts of relative arrivals and relative completions. These quantities allow us to tractably capture the transient correlational effect of the arrival and service processes on the mean queue length.