Queueing analysis of a statistical multiplexer with multiple slow terminals
SIGCOMM '91 Proceedings of the conference on Communications architecture & protocols
Packet delay and queue length for statistical multiplexers with low-speed access lines
Computer Networks and ISDN Systems
Correlation effects in ATM queues due to data format conversions
Performance Evaluation
Discrete-Time Models for Communication Systems Including ATM
Discrete-Time Models for Communication Systems Including ATM
Modeling Web Server Traffic with Session-Based Arrival Streams
ASMTA '08 Proceedings of the 15th international conference on Analytical and Stochastic Modeling Techniques and Applications
NET-COOP '09 Proceedings of the 3rd Euro-NF Conference on Network Control and Optimization
Discrete-time buffer systems with session-based arrival streams
Performance Evaluation
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In this paper, we study a statistical multiplexer which is modelled as a discrete-time single-server infinite-capacity queueing system. This multiplexer is fed by messages generated by an unbounded population of users. Each message consists of a generally distributed number of fixed-length packets. We assume the packet arrival process to exhibit simultaneously the following two types of correlation. First, the messages arrive to the multiplexer at the rate of one packet per slot, which results in what we call a primary correlation in the packet arrival process. Also, on a higher level, the arrival process contains an additional secondary correlation , resulting from the fact that the behaviour of the user population is governed by a two-state Markovian environment. Specifically, the state of this user environment in a particular slot determines the distribution of the number of newly generated messages in that slot. In previous work on this model, we provided analytical results for the moments and the tail distribution of the system contents. Using these results, we now concentrate on the message delay performance of this system, under the important assumption of a first-come-first-served queueing discipline for packets, whereby packets that arrive during the same slot are stored in random order. Closed-form expressions are derived for the mean value of both the total delay and the transmission time of an arbitrary message. Additionally, we provide a reasonably tight upper and lower bound for the tail probabilities of the message delay. By means of some numerical examples, we discuss the influence of the environment parameters on the delay performance.