Towards an Erlang formula for multiclass networks

Consider a multiclass stochastic network with state dependent service rates and arrival rates describing bandwidth-sharing mechanisms as well as admission control and/or load balancing schemes. Given Poisson arrival and exponential service requirements, the number of customers in the network evolves as a multi-dimensional birth-and-death process on a finite subset of Nk . We assume that the death (i.e. service) rates and the birth rates depending on the whole state of the system, satisfy a local balance condition. This makes the resulting network a so-called Whittle network and the stochastic process describing the state of the network is reversible with an explicit stationary distribution that is in fact insensitive to the service time distribution. Given routing constraints, we are interested in the optimal performance of such networks. We first construct bounds for generic performance criteria, that can be evaluated using recursive procedures, these bounds being attained in the cas...

• Type: Journal
• Year: 2010
• Where: QUESTA
• Authors: Matthieu Jonckheere, Jean Mairesse
• Keywords: Admission Control, QUESTA 2010, Rates, Service Rates