Lattice paths approach for transient solutions of M /G /1 queues using Coxian 2-phase distributio

Abstract

The paper aims at deriving transient solutions of non- Markovian queuing system M/G/1 starting from (k,0) to (m,n),m > n remaining below the barrier Y = X and does not include any idle time of server through lattice path approach. The explicit form of the density and other measures of the system performance are not known. Our approach is to approximate general service time with Coxian 2-phase distribution, C2 and represent the queuing process as a lattice path by recording the state of the system at the point of transitions. We use the lattice path combinatorics to count the feasible number of paths and corresponding probabilities. The above leads to the required density that has simple probabilistic structure and can be computed using R .The investigation of the influence of taking different values of a parameter on the behavior of the graphs of the density is also presented.