Queuing

The word queue is the common English term for “waiting line.” The study of queuing, or queuing theory, concerns how and why people or objects incur waiting. Waiting occurs in situations where servers are unable to provide immediate service for all requests. A classic queuing system is a ticket window at a movie theater. A waiting line forms when the rate of customers arriving to purchase tickets exceeds the cashier's rate of selling tickets. Not all queuing situations have an obvious line of waiting customers. Situations where people or objects are waiting for a server to arrive and provide service are also considered a queuing system. For example, during inclement weather a call for police to respond to a nonserious automobile accident represents a request for service that takes its place in a virtual waiting line.

Queuing is an integral part of most service operations. Because services cannot be “inventoried” ahead of time, some degree of waiting for an occupied server is likely to occur. In health care, queuing systems are commonplace. Some examples include (a) patients waiting for treatment in an emergency room, (b) hospital rooms waiting to be cleaned by housekeeping, (c) blood samples waiting to be processed through a lab, and (d) patient backlogs for surgical resources.

The term queuing system refers to a system in which waiting may occur. A queuing system is characterized by (a) a calling population,(b) an arrival process, (c) a queue configuration, (d) a queue discipline, and (e) a service process.

The term calling population refers to the group of customers or objects that may generate requests for service. For example, the calling population to an emergency room is the collection of all individuals in reasonable geographic proximity to the facility. In such a case, the calling population is very large and is modeled differently from a queuing system with relatively fewer people or objects potentially requesting service. For example, in a nursing unit the calling population consists only of those patients currently in the unit.

The term arrival process refers to the manner in which requests for service are generated from a calling population. Requests usually emerge in a random rather than predictable fashion. Characteristics of arrival processes include the rate and timing of requests, whether requests occur individually or in batches, and whether the calling population is homogeneous or contains subgroups. For example, the average rate of arrivals to an emergency department depends greatly on the day of week and time of day. Arrivals may occur individually or in batches (larger accidents) and may be subgrouped as requiring either critical or noncritical care.

[Page 477]The term queue configuration refers to the arrangement of queues and servers within a queuing system. The most common queue arrangements are either single line or multiline. Most grocery stores allow a separate queue to develop for each checkout, thus requiring a customer to choose which queue to join. Airline check-in counters, in contrast, often use a single waiting line in which customers are directed to the “next available agent.” Grocery stores often differentiate servers by offering an “express checkout” for customers with few items.

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