Study on Optimal Queue-Length-Threshold Scheduling Policy for an ATM Multiplexer with Finite Buffers and Natch Poisson Arrivals

This paper studies an optimal queue-length-threshold (QLT) scheduling policy for an ATM multiplexer with two types of traffic: real-time and nonreal-time. The proposed QLT scheduling policy is that if the number of queued nonreal-time packets is greater than or equal to a threshold value α, c2 servers are allocated to the nonreal-time traffic and the rest c1(=c−c2) servers are scheduled with priority policy that the real-time are given higher priority over the nonreal-time; otherwise all the c servers are scheduled with priority policy. The arrival process for each type of traffic is assumed to be batch Poisson with arbitrarily positive integer-valued probability distributions so as to describe the different bandwidth-requirement traffic from narrowband (NB) to wideband (WB). The multiplexer is modeled as a multiple synchronous-server system with separate finite buffers for each type of traffic. Performance measures are exactly derived by using a two-dimensional imbedded Markov-chain approach and the transition probabilities are exactly obtained via the application of residue theorem in complex variable. A trade-off between the effective measures of the two types of traffic is discussed under different (c2, α). Some performance criteria are defined to intend to determine an optimal QLT scheduling policy. This optimal QLT policy can indeed improve the performance criterion above 2–3% over the priority policy.