Network Calculus Delay Bounds in Multi-Server Queueing Networks with Stochastic Arrivals and Stochastic Services

Studies of multi-server networks are usually conducted on the assumptions of independent servers and specific arrivals, which may not capture the characteristics of realistic networks. In this paper, we propose a novel stochastic network calculus approach to perform delay analysis for a general multi-server network. The stochastic network service curves are derived in two ways with different assumptions. After that, we use these service curves to derive queueing delay bounds including delay bound distribution and mean delay bound for a specific scenario of which the classical M/M/N model is a subset. Compared with previous studies, it is worth highlighting that our analysis contains the cases where the arrival and service processes as well as the servers can either be independent or correlated. In addition, the accuracy of the analytical delay bounds are verified by comparing with the queueing theory results in an M/M/N model.