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Transient Analysis of a Single-Server Queue with Batch Arrivals Using Modeling and Functions Akin to the Modified Bessel Functions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Oduol, Vitalice |
| Copyright Year | 2009 |
| Abstract | Abstract — The paper considers a single-server queue with fixed-size batch Poisson arrivals and exponential service times, a model that is useful for a buffer that accepts messages arriving as fixed size batches of packets and releases them one packet at time. Transient performance measures for queues have long been recognized as being complementary to the steady-state analysis. The focus of the paper is on the use of the functions that arise in the analysis of the transient behaviour of the queuing system. The paper exploits practical modelling to obtain a solution to the integral equation encountered in the analysis. Results obtained indicate that under heavy load conditions, there is significant disparity in the statistics between the transient and steady state values. Keywords — batch arrivals, modelling, single-server queue, time-varying probabilities, transient analysis. I. system. I NTRODUCTION H E paper considers a single-server queue with fixed-size Poisson arrivals and exponential service times. This model is useful for a buffer that accepts messages arriving in fixed size batches of packets and releases one packet at time [1]. Justifications for the transient analysis of traffic in telecommunication systems abound [2]. It has long been recognized that transient performance measures for queues are complementary to the steady-state results [3-6] because there often exists a need to understand the initial behaviour of a system. In general queuing systems, arrivals at a service point (e.g. a switch) may occur in batches of different sizes. Due to congestion these arrivals may be queued for later forwarding to the destination. This paper considers the case in which the arrivals are of fixed size, and occur in continuous time. There may be cases where the network traffic is diverted suddenly to cope with faults, as in automatic protection switching (APS) in which the transport system re-directs traffic when faults and failures occur in subcomponents of the network. In such cases a service point may experience a sudden increase in its load, and this may continue until the original fault has been cleared. After the fault is corrected, traffic reverts to the previous distribution, and this presents another perturbation in the network. There exists now a reduction in the load in parts of the network, |
| Starting Page | 1728 |
| Ending Page | 1733 |
| Page Count | 6 |
| File Format | PDF HTM / HTML |
| Volume Number | 3 |
| Alternate Webpage(s) | https://waset.org/publications/4994/transient-analysis-of-a-single-server-queue-with-batch-arrivals-using-modeling-and-functions-akin-to-the-modified-bessel-functions |
| Alternate Webpage(s) | http://waset.org/publications/4994/transient-analysis-of-a-single-server-queue-with-batch-arrivals-using-modeling-and-functions-akin-to-the-modified-bessel-functions |
| Alternate Webpage(s) | http://www.waset.org/journals/waset/v33/v33-116.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
