It is therefore recommended that the management should provide more school buses in order to reduce the traffic congestion. 6 Multiple-Server Queues We will only consider the identical (homogenous) server case in which there are cidentical servers in parallel and there is just one waiting line (i.e., the queue is a single-channel queue). If a customer arrives when the queue is full, he/she is discarded (leaves the system and will not return). That is, there can be at most K customers in the system. This therefore indicates that the multiple servers’ model is more efficient than single server model as it minimizes these parameters. M/M/1/K Queueing Systems Similar to M/M/1, except that the queue has a finite capacity of K slots. The research revealed that the traffic intensity, average number of customers in the system, average number of customers in the queue, average time spent in the system, Average time spent in the queue of a single server and multiple servers are 0.9355,14.5, 13.5645,0.25, 0.2339 and 0.4677, 1.1974, 0.2619, 0.0206,0.0045 respectively. D Deterministic Service Rate (Constant rate) M/D/1 case (random Arrival, Deterministic service, and one service channel) Expected average queue length E(m) (2- 2)/ 2 (1- ) Expected average total time E(v) 2- / 2 (1- ) Expected average waiting time E(w) / 2 (1- ) M/M/1 case (Random Arrival, Random Service, and one service.
MULTI CHANNEL SYSTEMS QUEING THEORY MANUAL
The data was analyzed, using manual computations to validate the results. Primary data was employed using observation method in the course of conducting this research. The aim of this paper is to compare the parameters of single server and multiple servers’ models. Some suggestions for the future are given.This research work is based on queuing theory and its application analysis on bus services using single server and multiple servers’ models, a case study of Federal Polytechnic transport system, Kaura Namoda. Finally attention is given to how the methods derived could be extended to include all possible multi-channel, bulk-arrival and bulk-service queueing systems.
The concept of bulk-service is introduced and formulae derived for the mean number in the system for fixed arrival batch sizes and probabilistic arrival batch sizes. Probabilistic arrival batch size distributions are then considered, and a recursive approximation developed to the mean number in the system. For systems with a fixed arrival batch size two methods are derived to approximate the mean number in the system, one simple straight line based method and one, more complicated, quadratic based approach. In this study, single-channel and multi-channel queuing theory (M/M/s: FCFS). Multi-channel, bulk arrival systems are then considered. Queue management systems are specially designed for banks allowing them to. An approximation will be formulated to the mean number of a multi-channel simple queueing system based on the mean number in a single-channel simple queueing system. Section 19.3 guides the reader to simulate a mobile. Especially important is the empha-sis on the insensitivity property of models such as M/M/1, M/M/k/k, processor sharing and multi-service that lead to practical and robust approximations as described in Chapters 7, 8, 13, and 14. An introduction will be given to the subject area and the relevant literature will be reviewed. utilization issues of a multi-channel system are presented. The aim of this thesis is to provide the practitioner with a straightforward and reasonably accurate mans of calculating the expected number in the system. In particular attention is focused on approximating the expected number in the queueing system in a steady state. This thesis deals with an area of queueing theory which, despite its obvious applicability to real-life, has received relatively little attention in the literature, the field of bulk-arrival, bulk-service, multi-channel queueing systems.
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