A matrix-analytic solution for the DBMAP/PH/1 priority queue

Abstract

Priority queueing models have been commonly used in telecommunication systems. The development of analytically tractable models to determine their performance is vitally important. The discrete time batch Markovian arrival process (DBM AP ) has been widely used to model the source behavior of data traffic, while phase-type (P H) distribution has been extensively applied to model the service time. This paper focuses on the computation of the DBM AP/P H/1 queueing system with priorities, in which the arrival process is considered to be a DBM AP with two priority levels and the service time obeys a discrete P H distribution. Such a queueing model has potential in performance evaluation of computer networks such as video transmission over wireless networks and priority scheduling in ATM or TDMA networks. Based on matrix-analytic methods, we develop computation algorithms for obtaining the stationary distribution of the system numbers and further deriving the key performance indices of the DBM AP/P H/1 priority queue.

Efficient analysis of the queue length moments of the MMAP/MAP/1 preemptive priority queue

“…Due to the structure of matricesĀ 0 , A − and R, (17) is equivalent to the solution of an M/G/1 type CTMC (see [3] and [6]). However, by using the relation RA − = A + G (see e.g.…”

“…The discrete time version of this queue is solved by Alfa following a matrix geometric approach in [1] and [2]. The extension of these results with batch arrivals are presented in [3]. The non-preemptive priority case with general service time and no correlation between the classes is considered in [4] and [5], where generator functions are derived for the queue length and the waiting time distributions in Laplace transform domain.…”

Time-dependent performance analysis of a discrete-time priority queue

“…In the recent literature, emphasis is put on more complex priority queueing models. Examples are multi-server priority queueing models [6,9], priority queueing models with correlation in the arrival process [3,13,15,20,22,24], priority queueing models with acceptance control [1,4] and priority models with server vacations [8].…”

Partially shared buffers with full or mixed priority

“…In this paper, class-1 and class-2 arrivals are modelled by means of a 2-class discrete-time batch Markovian arrival process (2-DBMAP). As we need to keep track of the entire sequence of arrivals, the definition of this process is more general than the standard one [19]. In the current contribution, a 2-DBMAP is completely characterized by the Q×Q matrices A(x) governing the transitions from slot to slot of the underlying discrete-time Markov chain when arrivals occur according to the sequence x ∈ Ω.…”

“…Here, information about the order of arrivals is removed from the arrival process but assumed to be generally known. This enables writing the arrival process as a standard 2-DBMAP [19] given by…”