The Elements of a Queuing System Are



The Calling Population

  • The population of potential customers, referred to as the calling population, may be assumed to be finite or infinite.

  • For Example: Consider a group of five tire-curing devices. A machine opens after a certain amount of time and requires the assistance of a worker who removes the tyre and replaces it with an uncured tyre. The "customers" are the machines, who "arrive" when they automatically open. The worker is the "server," who as quickly as possible "serves" an open machine. The calling population is limited to five machines and is finite.

  • The calling population is commonly believed to be finite or infinite in systems with a massive number of potential clients. Potential consumers of a restaurant, bank, or other business are examples of infinite populations.

  • The way the arrival rate is defined is the major distinction between finite and infinite population models. The number of consumers who have left the calling population and joined the queueing system has no effect on the arrival rate in an infinite-population model. The arrival rate to the queueing system, on the other hand, is dependent on the number of consumers being served and waiting in finite calling population models.

System Capacity

  • In many queueing systems there is a limit to the number of customers that may be in the waiting line or system. An automatic vehicle wash, for example, may only have room for 10 automobiles in line to access the machine.

  • When a consumer arrives and discovers the system is full, he or she does not enter and quickly returns to the calling population.

  • Some systems, such as student concert ticket sales, may be deemed to have infinite capacity. There are no restrictions on the number of students who can wait to get tickets.

  • When a system's capacity is restricted, a distinction is made between the arrival rate (i.e., the number of arrivals per time unit) and the effective arrival rate (i.e., the number of arrivals per time unit) (i.e., the number who arrive and enter the system per time unit).

The Arrival Process

  • Interarrival periods of successive consumers are commonly used to describe the arrival process in infinite-population models. Arrivals might happen at predetermined periods or at random. Interarrival times are commonly characterized by a probability distribution when at random times.

Queue Behavior and Queue Discipline

  • Customers' actions while waiting for service are referred to as queue behavior. In some cases, incoming consumers may bulk (leave when they realize the queue is too long), renege (leave after being in the line when they see the line is moving too slowly), or jockey (leave after being in the line when they find the line is moving too slowly) (move from one line to another if they think they have chosen a slow line).

  • When a server becomes available, queue discipline determines which customer will be chosen for service based on the logical ordering of customers in the queue.

Service Times and the Service Mechanism

  • S1, S2, S3... are the service times of succeeding arrivals. They can last for a long time or for a short time. In various scenarios, the exponential, Weibull, gamma, lognormal, and truncated normal distributions have all been effectively utilized as models of service times.