Queuing theory deals with problems that involve waiting (or queuing). It is quite common that instances of queue occur every day in our daily life. Examples of queues or long waiting lines might be:
Waiting for service in banks and at reservation counters.
Waiting for a train or a bus.
Waiting for checking out at the Supermarket.
Waiting at the telephone booth or a barber’s saloon.
Whenever a customer arrives at a service facility, some of them usually have to wait before they receive the desired service. This forms a queue or waiting for line and customers feel discomfort either mentally or physically because of the long waiting queue.
We infer that queues form because the service facilities are inadequate. If service facilities are increased, then the question arises how much to increase? For example, how many buses would be needed to avoid queues? How many reservation counters would be needed to reduce the queue? The increase in a number of buses and reservation counters requires additional resource. At the same time, costs due to customer dissatisfaction must also be considered.
In designing a queuing system, the system should balance service to customers (short queue) and also the economic considerations (not too many servers). Queuing theory explores and measures the performance in a queuing situation such as an average number of customers waiting in the queue, average waiting time of a customer and average server utilisation.
The customers arrive at service counter (single or in groups) and are attended by one or more servers. A customer served leaves the system after getting the service. In general, a queuing systems comprises two components, the queue and the service facility. The queue is where the customers are waiting to be served. The service facility is customers being served and the individual service stations.
Characteristics of Queuing System
In designing a good queuing system, it is necessary to have a good information about the model. The characteristics listed below would provide sufficient information.
1. The arrival pattern.
2. The service mechanism.
3. The queue discipline.
4. The number of customers allowed in the system.
5. The number of service channels.
The Arrival Pattern
The arrival pattern describes how a customer may become a part of the queuing systems. The arrival time for any customer is unpredictable. Therefore, the arrival time and the number of customers arriving at any specified time intervals are usually random variables. A Poisson distribution of arrivals corresponds to arrivals at random. In Poisson distribution, successive customers arrive after intervals which independently are and exponentially distributed. The Poisson distribution is important, as it is a suitable mathematical model of many practical queuing systems as described by the parameter “the average arrival rate”.
The Service Mechanism
The service mechanism is a description of resources required for service. If there are an infinite number of servers, then there will be no queue. If the number of servers is finite, then the customers are served according to a specific order. The time taken to serve a particular customer is called the service time. The service time is a statistical variable and can be studied either as the number of services completed in a given period of time or the completion period of a service.
The Queue Discipline
The most common queue discipline is the “First Come First Served” (FCFS) or “First-in, First-out” (FIFO). Situations like waiting for a haircut, ticket booking counters follow FCFS discipline. Other disciplines include “Last In First Out” (LIFO) where the last customer is serviced first, “Service In Random Order” (SIRO) in which the customers are serviced randomly irrespective of their arrivals. “Priority service” is when the customers are grouped into priority classes based on urgency. “Preemptive Priority” is the highest priority given to the customer who enters into the service, immediately, even if a customer with lower priority is in service. “Non-preemptive priority” is where the customer goes ahead in the queue but will be served only after the completion of the current service.
The Number of Customers allowed in the System
Some of the queuing processes allow the limitation to the capacity or size of the waiting room so that the waiting line reaches a certain length, no additional customers is allowed to enter until space becomes available by a service completion. This type of situation means that there is a finite limit to the maximum queue size.