étude de l'attente prioritaire dans les ports
Résumé
Queuing systems are prevalent throughout society. The adequacy of these systems can have an important effect on the quality of live and productivity. Queuing theory studies queuing systems by formulating mathematical models of their operation and then using these models to derive measures of performance. This analysis provides vital information for effectively designing queuing systems that achieve an appropriate balance between the cost of providing a service and the cost associated with waiting for that service. The exponential distribution plays a fundamental role in queuing theory for representing the distribution of interarrival and service times, because this assumption enables us to represent the queuing system as a continuous time Markov chain. For the same reason, phase-type distributions such as the Erlang distribution, where the total time is broken down into individual phases having an exponential distribution, are very useful. Priority -discipline queuing models are useful for the common situation where some categories of customers (ships) are given priority over other for receiving service. We consider a single server queue with two classes of customers (ships), each having its fixed entry fee. We show that profit and social welfare may benefit from a service discipline based on relative priorities. The analysis of a preemptive priority queuing system with K (≥ 2) classes of jobs is undertaken. The system consists of a single processor representing a model of discrete dynamic scheduling problems associated with ( Mk / Gk / 1 / ∞) endogenous priority queues. The processor schedules jobs which arrive according to a Markov arrival process. The process of service is arbitrary. With each job are associated particular endogenous dynamic priorities, called scheduling by “mean bounded priorities with arrival pattern” (MBPAP). The main goal is, for the case of an arrival pattern of jobs, to present an original scheduling strategy, to derive the waiting time wk (t) and to discuss the implementation of the priorities. This queuing system is investigated. We develop a queuing simulation algorithm that systematically adjusts the number of servers in a system. It applies to systems with a single waiting line but multiple servers. We impose a few realistic assumptions then use the algorithm to simulate random Poisson arrivals and exponential service. The results show that the proposed algorithm increases the systems efficiency and customer (ships) satisfaction relative to existing models. In fact, several thousand research papers formulating and /or analysing queuing models have already appeared in the technical literature, and many more are being published each year!
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