queuingtheory-100903073424-phpapp02 - QUEUING THEORY...

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QUEUING THEORY Introduction Queuing theory deals with problems that involve waiting (or queuing). It is quite common that instances of queue occurs everyday in our daily life. Examples of queues or long waiting lines might be Waiting for service in bank and at reservation counter. Waiting for a train or bus. Waiting at barber saloon. Waiting at doctors’ clinic. Whenever a customer arrives at a service facility, some of them usually have to wait before they receive the desired service. This form a queue or waiting line and customer feel discomfort either mentally or physically because of long waiting queue. We infer that queues from because the service facilities are inadequate. If service facilities are increased, then the question arise how much to increase? For example, how many buses would be needed to avoid queues? How many reservation counters would be needed to reduce the queue? Increase in number of buses and reservation counters requires additional resources. At the same time, cost due to customer dissatisfaction must also be considered. Symbols and notations : n = total number of customers in the system, both waiting and in service µ = average number of customers being serviced per unit of time. λ = average number of customers arriving per unit of time. C = number of parallel service channels L s or E(n) = average number of customers in the system, both waiting in the service. L q or E(m) = average number of customers waiting in the queue W s or E(w) = average wating time of a customer in the system both waiting and in service W q or E(w) = average waiting time of a customer in the queue P n (t = probability that there are n customer in the queue total cost of the system cost cost of service
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cost of waiting optical service level level of service Queuing system The customers arrive at service counter (single or in a group) and attended by one or more servers. A customer served leaves the system after getting the service. In general, a queuing system comprise with two components, the queue and the service facility. The queue is where the customers are waiting to be served. The service facility is customers being served and the individual service stations. SERVICE SYSTEM The service is provided by a service facility (or facilities). This may be a person (a bank teller, a barber, a machine (elevator, gasoline pump), or a space (airport runway, parking lot, hospital bed), to mention just a few. A service facility may include one person or several people operating as a team. There are two aspects of a service system—(a) the configuration of the service system and (b) the speed of the service. Configuration of the service system The customers’ entry into the service system depends upon the queue conditions. If at the time of customers’ arrival, the server is idle, then the customer is served immediately. Otherwise the customer is asked to join the queue, which can have several configurations. By configuration of the service
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This note was uploaded on 12/13/2010 for the course EE 131 taught by Professor Smith during the Spring '10 term at Florida State College.

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queuingtheory-100903073424-phpapp02 - QUEUING THEORY...

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