Stochastic Models for Communication Networks with Moving Customers

Models of integrated services data networks with moving customers (e.g., mobiles with calls in progress) and level dependent spatial Markov-additive processes of arrivals are considered. It is assumed that waiting is not allowed and, accordingly, two types of service models are examined: with infinite number of servers and loss models with finite number of servers. In general, arrivals can be of different types. In all models, service times have arbitrary distribution functions. Basic characteristics of interest are marginal and joint distributions of numbers of customers being served in disjoint spatial subsets. For this characteristics, we derive differential equations and, in some particular cases, obtain their explicit expressions.