Management of Waiting Lines
CHAPTER 18
Management of WAITING LINES
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 18-6 in the text follows this somewhat (e.g., average number running). Other examples of finite source systems include passengers on a plane
Management of WAITING LINES
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 18-6 in the text follows this somewhat (e.g., average number running). Other examples of finite source systems include passengers on a plane