Feasibility of serving packet streams with delay and loss requirements

The feasibility of serving packet streams with diverse delay and loss requirements over a single channel is examined. Specifically, the following problem is discussed, where a discrete-time formulation is adopted: There is a communication channel with a time-varying capacity, the capacity of the channel changes according to a random process with known statistics. A set of streams are incident on that channel, and are needed to be transmitted with some delay and loss requirements, as explained subsequently. Packet arrivals in streams are also modeled as some suitable random processes with known statistics, it is assumed for the simplicity of exposition that at most one packet arrives in any stream at any time. Any packet in stream i, arriving at time a, is required to be transmitted at only one of the time instances { a, a + 1, a + 2,…, a + di} for some finite non-negative integer d i, if it is ever to be transmitted. All packets being transmitted should satisfy this constraint. A packet not being transmitted is discarded, and said to be terminated. All other packets are considered being successfully transmitted. The rate of successful transmissions, called the success rate, for stream i is roughly the asymptotic ratio of the number of packets being transmitted to the total number of packets in stream i, as time goes to infinity. A tuple of success rates over all the streams is said to be feasible, roughly, if there exists a scheduling delivering the success rates, with probability 1. A scheduling is a mapping of all the packets to be transmitted into the positive integers, where the number of packets being mapped into n does not exceed the capacity of the channel at time n. The region of all feasible success rate tuples is called as the feasible region. The problem is to find the feasible region, given all the necessary specifications. A graph-theoretic approach is taken for solving the above problem. A matching problem (V-cover-constrained Matching Problem) on graphs is formulated, and a special case of V-partition-constrained Matching Problem on bipartite graphs is solved. (Abstract shortened by UMI.)