Service Characteristics Essays - Stochastic Processes,

Service Characteristics 1. Service Mechanism or Process: For each category of customer it is necessary to describe the service process. This is usually expressed as a probability distribution for service times; for example, service times might be normally distributed or uniformly distributed. At the least, we need to state the average time it takes for a server to serve a customer and the variance or standard deviation of the service time. We decline = average service rate possible per server in customers/unit time so 1/ is the average service time. 2. Queue Discipline When customers are in the queue, the system must have operating rules that determine which customer to serve next; these rules are called the queue discipline. Frequently, we assume that the queue discipline is first-come-first-served (FCFS) System Configuration 1. Number, Type, and Configuration of Servers Number of servers in the system. Everything being equal, the more servers available, the less waiting time. Type of servers used. We may choose between two types of machines, or combinations of people and machines, that have different average service rates and different variances in service times. Queuing analysis can help us determine whether a faster or less variable server is worth extra cost. The configuration of servers. For example, should the system have dedicated servers ? only certain customers can use certain servers. 2. Queue Capacity Another design variable is the maximum number of customers that can be put in the queue before additional customers must be turned away. For example, a normal telephone has a queue capacity of zero. When the phone is being used (a caller is being served), additional incoming calls cannot enter the queue; they receive a busy signal and are turned away. Phone systems can, however, be designed so that incoming calls are put ?on hold? in a queue. 3. Number of Queues Whether each server has its own queue or all servers share a single queue can affect not only the average waiting time, Btu also the distribution and equity of waiting times as will be shown later. Steady state: When the rate of departures from the system equals the rate of arrivals. This implies that any start-up or shutdown (called transient) effects are eliminated. For example, when a bank opens in the morning all servers are available, so the amount of waiting in the queue is reduced, but there will also be some time lag until customers begin to leave the system. Utilization factor measures how much of the queuing system capacity is actually utilized serving customers. The simplest queuing system that includes randomness is the M/M/I system. It is based on the following assumptions. 1. Arrivals are generated by a Poisson process 2. Service times are exponentially distributed 3. There is one server 4. Any queue discipline can be used 5. Queue capacity is infinite 6. The customer population is homogenous and infinite in size 7. Customers are well behaved; no balking or reneging occurs. Benefits of pooling servers into one system If customers ore homogeneous (with respect to their service time distributions), then there will be less customer waiting on average if servers are pooled into one queuing system, rather than having a separate one-server system for each population of customers. The Number of Queues for multiserver systems Using a single waiting line for several servers is usually more efficient, and it is perceived by customers as being more equitable than having separate waiting lines for each server. Even when a single queue is practical, it may not be most efficient, especially when the customers and servers are people. There are at least four factors that in some cases may make separate waiting lines for each server preferable to a single queue. 1. With separate queues, servers are sometimes able to serve to two customers at once 2. The time it takes for a customer to move from a common queue to the server may be longer than with individual queues for each server. 3. Servers sometimes work faster when they have their own queue, the customers in their queue are their customers and they are sensitive to the waiting incurred, whereas with a single queue the customer-server relationship is depersonalized until service begins and there is less sense of an obligation to serve customers quickly. 4. With separate queues, customers can choose their server. In some