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Waiting Lines -- Supplement to Chapter: Simulation

Key Ideas

1. Waiting lines are an important consideration in capacity planning. Waiting lines tie up additional resources (waiting space, time, etc.); they decrease the level of customer service: and they require additional capacity to reduce them.

2. Waiting lines occur whenever demand for service exceeds capacity (supply). Even in systems that are underloaded, waiting lines tend to form if arrival and service patterns are highly variable because the variability creates temporary imbalances of supply and demand.

3. All of the waiting line models presented in the chapter (except the constant service time model) assume, or require, that the arrival rate can be described by a Poisson distribution and that the service time can be described by a negative exponential distribution. Equivalently, we can say that the arrival and service rates must be Poisson, and the interarrival time and the service time must be exponential. In practice, one would check for this using a statistical Chi Square test: for problems provided here and in the textbook, assume that these distributions hold. Note that if these assumptions are not met, alternate approaches (e.g., intuition, simulation, other models) should be considered.

4. Much can be learned about the behavior of waiting lines by modeling them. A wide variety of models are presented in the text, different models pertain to different system characteristics.

5. A major distinction in waiting line models relates to whether the number of potential arrivals to the system is limited (finite) or unlimited (infinite). Perhaps the classic example of a finite source system is the machine, repairperson problem, wherein the server or servers handle calls for repairs on a small, fixed number of machines. Note that the definition of terms in Table 17-6 in the text follows this somewhat (e.g., average number running). Other examples of finite source systems include passengers on a plane who might request assistance or information from a steward or stewardess, a sales rep who handles a small set of customers, and a telephone operator who places outgoing calls for residents of a small hotel. Examples of infinite-source systems are plentiful: service stations, banks, post offices, restaurants, theaters, supermarkets, libraries, stop signs, and telephone switchboards.

6. Once a situation has been modeled and the relevant data gathered (e.g., an-arrival rate, service time, number of servers, etc.), formulas and/or tables can be used to obtain information about the system such as the expected number waiting for service, the expected waiting time, the maximum line length, system utilization, and so on. This information can be used to compare various system alternatives (e.g., one server versus two servers, different equipment possibilities, and so on) with respect to cost and impact on waiting times, etc.

7. The goal in queuing analysis is to develop a system in which the sum of capacity costs and waiting costs is minimized. Sometimes this goal may be taken in an absolute sense or the goal may be to minimize total costs given a minimum level of customer service specified by management.

8. Most of the models described in the chapter assume arrivals are processed on a first-come, first-served basis (FCFS). Many examples of FCFS exist. Sometimes, however, customers are processed on a priority basis rather than FCFS. That is, late arriving customers may be processed ahead of those already waiting. A hospital emergency room is an example; seriously ill or injured persons are attended to while less seriously ill persons wait. A key difference in the multiple priority model compared to other models is computation of average waiting times, and average number waiting, for each of the classes or categories of waiting customers.










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