G-Queue as a Computable Node Model: Steady State Solution, Applications and Extensions

This is a homogeneous multi-server FCFS queue with finite or infinite queueing capacity. The service time distribution at a server is generalised exponential. The arrival process is the superposition of K independent compound Poisson processes (CPPk ; k = 1, 2, . . . ,K) of (positive) customers and a CPP of negative customers. All the arrival and the service processes are jointly modulated by an N -state Markov phase process. Exact solutions to the steady state joint probabilities of queue length by phase are derived. The use of negative customers (with the RCE-immune servicing killing discipline or another) is to provide a platform for many possible studies including load-balancing and the effect of server-breakdowns. This complex queue, capable of representing correlations and burstiness of incoming traffic, capable of handling large batch sizes of geometric or non-geometric distribution in both arrivals and services, with its viable and efficient steady-state solution, can provide a basis for finding an appropriate as well as computable model for nodes in optical networks.