The very rapidly spreading and upgrading of telecommunications and computer technology has led to combination and simultaneous maintenance of inter-generational systems. A number of illustrative examples show interesting properties of the systems operating under the introduced policies and their performance characteristics. This dependence can be neglected by using a heuristic threshold policy. Then, we show that the optimal allocation policy between the servers within each queue is of threshold type with threshold levels depending on the queue length and phase of an arrival process. As an alternative static policy, we consider an optimal Bernoulli splitting which prescribes the optimal allocation probabilities.

We discuss here the algorithm to calculate the optimal routing policy based on specially constructed Markov-modulated Poisson processes.

An open-loop control assumes the static resource allocation when a router has no information about the state of the system. Heterogeneity implies different servers in terms of speed of service. In this paper, we study the problem of optimal routing for the pair of two-server heterogeneous queues operating in parallel and subsequent optimal allocation of customers between the servers in each queue.

Mathematica for loop examples