Analysis of Stationary Queue Length Distribution for Geo/T-IPH/1 Queue

Analysis of Stationary Queue Length Distribution for Geo/T-IPH/1 Queue

In this paper we study a Geo/T-IPH/1 queue model, where T-IPH denotes the discrete time phase type distribution defined on a birth-and-death process with countably many states. The queue model can be described by a quasi-birth-anddeath (QBD) process with countably phases. Using the operator-geometric solution method, we first give the expression of the operator and the joint stationary distribu...

Contents Stationary Queue Length Distribution for M / M / 1 / K Queue with Preemptive Priorities 6

This paper analyses a multiple class single server M/M/1/K queue with finite capacity under preemptive service priority discipline. The Poisson process has been used to model the multiple classes of arrival streams. The service times have exponential distribution. Analytical expressions for the flow balanced equations have been derived using Markov chain. This paper presents an analytical solut...

Second Moment of Queue Size with Stationary Arrival Processes and Arbitrary Queue Discipline

In this paper we consider a queuing system in which the service times of customers are independent and identically distributed random variables, the arrival process is stationary and has the property of orderliness, and the queue discipline is arbitrary. For this queuing system we obtain the steady state second moment of the queue size in terms of the stationary waiting time distribution of a s...

Bmap/g/1 Queue under D-policy: Queue Length Analysis

Stationary remaining service time conditional on queue length

In Mandelbaum and Yechiali (1979) a simple formula is derived for the expected stationary remaining service time in a FIFO M/G/1 queue, conditional on the number of customers in the system being equal to j, j ≥ 1. Fakinos (1982) derived a similar formula using an alternative method. Here we give a short proof of the formula using rate conservation law (RCL), and generalize to handle higher mome...