Analysis of priority queues with session-based arrival streams

In this paper, we analyze a discrete-time priority queue with session-based arrivals. We consider a user population, where each user can start and end sessions. Sessions belong to one of two classes and generate a variable number of fixed-length packets which arrive to the queue at the rate of one packet per slot. The lengths of the sessions are generally distributed. Packets of the first class have transmission priority over the packets of the other class. The model is motivated by a web server handling delay-sensitive and delay-insensitive content. By using probability generating functions, some performance measures of the queue such as the moments of the packet delays of both classes are calculated. The impact of the priority scheduling discipline and of the session nature of the arrival process is shown by some numerical examples

Session delay in file server output buffers with general session lengths

In this paper, we analyze the delay incurred by session-based traffic in the output buffer of a file server. Users can start and end sessions during which they are active and download information from the file server. Per time slot, each active user downloads a random but strictly positive number of information packets. Each session lasts for a random, yet again, strictly positive number of slots. We model the file server output buffer as a discrete-time infinite-capacity queueing system and we present an analytical technique to study the queueing delay for sessions in case of a general session-length distribution. The analysis method is based on the combination of a generating-functions approach with the use of an infinite-dimensional state description. As a result, a closed-form expression for the mean session delay is obtained. The analysis is illustrated with a numerical example, based on real traces of file server traffic

Performance analysis of buffers with train arrivals and correlated output interruptions

In this paper, we study a discrete-time buffer system with a timecorrelated packet arrival process and one unreliable output line. In particular, packets arrive to the buffer in the form of variable-length packet trains at a fixed rate of exactly one packet per slot. The packet trains are assumed to have a geometric length, such that each packet has a fixed probability of being the last of its corresponding train. The output line is governed by a Markovian process, such that the probability that the line is available during a slot depends on the state of the underlying J-state Markov process during that slot. First, we provide a general analysis of the state of the buffer system based on a matrix generating functions approach. This also leads to an expression for the mean buffer content. Additionally, we take a closer look at the distributions of the packet delay and the train delay. In order to make matters more concrete, we next present a detailed and explicit analysis of the buffer system in case the output line is governed by a 2-state Markov process. Some numerical examples help to visualise the influence of the various model parameters

On deciding stability of multiclass queueing networks under buffer priority scheduling policies

One of the basic properties of a queueing network is stability. Roughly speaking, it is the property that the total number of jobs in the network remains bounded as a function of time. One of the key questions related to the stability issue is how to determine the exact conditions under which a given queueing network operating under a given scheduling policy remains stable. While there was much initial progress in addressing this question, most of the results obtained were partial at best and so the complete characterization of stable queueing networks is still lacking. In this paper, we resolve this open problem, albeit in a somewhat unexpected way. We show that characterizing stable queueing networks is an algorithmically undecidable problem for the case of nonpreemptive static buffer priority scheduling policies and deterministic interarrival and service times. Thus, no constructive characterization of stable queueing networks operating under this class of policies is possible. The result is established for queueing networks with finite and infinite buffer sizes and possibly zero service times, although we conjecture that it also holds in the case of models with only infinite buffers and nonzero service times. Our approach extends an earlier related work [Math. Oper. Res. 27 (2002) 272--293] and uses the so-called counter machine device as a reduction tool.Comment: Published in at http://dx.doi.org/10.1214/09-AAP597 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org