Insensitive Bandwidth Sharing in Data Networks
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This paper presents a unified model of classical teletraffic models covering both circuit-switched and packet-switched networks. The models of Erlang, Engset, Palm, and Delbrouck are generalized to loss and delay systems with multi-rate BPP (Binomial, Poisson, Pascal) traffic streams which all are insensitive to the holding time distributions. The Engset and Pascal traffic streams are also insensitive to the idle time distribution. Engset traffic corresponds to a finite number of users and Pascal traffic results in same state probabilities as Pareto-distributed inter-arrival times. The model is similar to balanced fair scheduling by Bonald and Proutière, but the approach is much simpler and allows for explicit results for finite source traffic and performance measures of each individual service. The model is evaluated by a simple stable algorithm with a minimal memory requirement and a time requirement which is linear in number of streams and number of servers plus queueing positions.