Calculating steady-state probabilities of single-channel queueing systems with changes of service times depending on the queue length

An algorithm for calculating steady state probabilities of $M|E_r|c|K$ queueing systems

This paper presents a method for calculating steady state probabilities of M |Er|c|K queueing systems. The infinitesimal generator matrix is used to define all possible states in the system and their transition probabilities. While this matrix can be written down immediately for many other M |PH |c|K queueing systems with phase-type service times (e.g. Coxian, Hypoexponential, . . . ), it requi...

Steady State Probabilities of a Three Preemptive Single Server Queue

Steady-State Queue Length Analysis of a Batch Arrival Queue under N-Policy with Single Vacation and Setup Times

This paper investigates the steady state property of queue length for a batch arrival queue under N-policy with single vacation and setup times. When the system becomes empty, the server is turned off at once and takes a single vacation of random length V . When he returns, if the queue length reaches or exceeds threshold ( 1) N N  , the server is immediately turned on but is temporarily unava...

Tail Behaviour of the Area Under the Queue Length Process of the Single Server Queue with Regularly Varying Service Times

This paper considers a stable GI|GI|1 queue with a regularly varying service time distribution. We derive the tail behaviour of the integral of the queue length process Q(t) over the busy period. We show that an occurrence of a large integral is related to an occurrence of a large maximum of the queueing process over the busy period and we exploit asymptotic result for this variable. We also pr...

Steady - State Analysis of a Queue with Varying Service RateR

In this paper we study a queueing model with a server that changes its service rate according to a nite birth and death process. The object of interest is the simultaneous distribution of the number of customers in the system and the state of the server in steady-state. The model can be applied to the performance analysis of (low priority) Available Bit Rate (ABR) traac at an ATM switch in the ...