Queuing System Essay

638 WordsDec 19, 20133 Pages
Queuing System Introduction Analytic congestion models A congestion system is system in which there is a demand for resources for a system, and when the resources become unavailable, those requesting the resources wait for them to become available. The level of congestion in such systems is usually measured by the waiting line, or queue, of resource requests (waiting line or queuing models). Elements of a queuing system Arrival process Distributed of time between arrival of successive customers; Inter-arrival time could generally be exponential distributed or constant. Exponentially distributed: If an arrival just occurred or if we have been waiting 20 minutes for an arrival, the probability of an arrival the next 5 minutes remains the same. It can be shown that the only continuous random variable that is memoryless is the exponentially distribution. It can also be shown that if the time between arrivals is exponentially distributed with mean, then the distribution of the number of arrivals during time interval is a Poisson distributed with mean 1/(. Other characteristics of an arrival process include whether the customer population is finite or infinite and whether the mean time between arrivals is constant or changing over time. If the population of customers is finite, the rate of customer arrivals as the number of customers in the system increases. Service process The service process is characterized by the distribution of the time to service an arrival and the number of services. Models of congestion system often assume that the service time is exponentially distributed, thereby facilitating the development of analytical models of the congestion system. The number of serviced is greater that the rate at which customers arrive. Traffic intensity (() = rate at which customers arrive/ rate customers can be

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