Asymptotics of waiting time distributions in the accumulating priority queue

Queueing Systems - We analyze the asymptotics of waiting time distributions in the two-class accumulating priority queue with general service times. The accumulating priority queue was suggested by...     

Analysis of Stop-and-Wait ARQ for a wireless channel

In this paper, we study the behavior of the transmitter buffer of a system working under a Stop-and-Wait retransmission protocol. The buffer at the transmitter side is modeled as a discrete-time infinite-capacity queue. The numbers of information packets entering the buffer during consecutive slots are assumed to be independent and identically distributed random variables. The packets are sent over an unreliable channel and transmission errors occur in a correlated manner. Specifically, the probability of an erroneous transmission is modulated by a two-state Markov chain. An expression is derived for the probability generating function of the buffer content. This expression is then used to derive several queue-length characteristics and the mean packet delay. Numerical examples illustrate the strong effect of error correlation on the system performance. The obtained analytical results are also compared with appropriate simulations.      

Delay and partial system contents for a discrete-time G-D-c queue

We consider a discrete-time multiserver queueing system with infinite buffer size, constant service times of multiple slots and a first-come-first-served queueing discipline. A relationship between the probability distributions of the partial system contents and the packet delay is established. The relationship is general in the sense that it doesn’t require knowledge of the exact nature of the arrival process. By means of the relationship, results for the distribution of the partial system contents for a wide variety of discrete-time queueing models can be transformed into corresponding results for the delay distribution. As a result, a separate full analysis of the packet delay becomes unnecessary.      

Queueing models for the analysis of communication systems

Queueing models can be used to model and analyze the performance of various subsystems in telecommunication networks; for instance, to estimate the packet loss and packet delay in network routers. Since time is usually synchronized, discrete-time models come natural. We start this paper with a review of suitable discrete-time queueing models for communication systems. We pay special attention to two important characteristics of communication systems. First, traffic usually arrives in bursts, making the classic modeling of the arrival streams by Poisson processes inadequate and requiring the use of more advanced correlated arrival models. Second, different applications have different quality-of-service requirements (packet loss, packet delay, jitter, etc.). Consequently, the common first-come-first-served (FCFS) scheduling is not satisfactory and more elaborate scheduling disciplines are required. Both properties make common memoryless queueing models (M/M/1-type models) inadequate. After the review, we therefore concentrate on a discrete-time queueing analysis with two traffic classes, heterogeneous train arrivals and a priority scheduling discipline, as an example analysis where both time correlation and heterogeneity in the arrival process as well as non-FCFS scheduling are taken into account. Focus is on delay performance measures, such as the mean delay experienced by both types of packets and probability tails of these delays.