The waiting line is a list of customers who remains waiting for getting certain goods or services from service center. Understanding waiting lines or queues and learning how to manage them is one of the most important areas in operation management. In organizations or in personal life, there are examples of processes which generates waiting lines or queues. Such waiting lines occur because the current services facility is insufficient to provide service at that instance. For examples: on traveling by airplanes, we have first had experiences with several types of waiting lines (queues). To buy tickets, we may have to stand in line at travel agent's office. When we arrive at airport we stand in line to check baggage then we stand in line again to get a seat assignment. We line up again (once more) for a security check and the again in the boarding lounge before entering the airplane. When we are inside the plane, we wait for those ahead of us to take their seats. The plane it self waits for take off clearance, when it arrives at its destination it may circle sometime waiting for landing clearance. And finally, we may wait for baggage to arrive and then for ground transportation.
The goal of queuing is essentially to minimize total costs. There are two basic categories of cost in a queuing situation: - i) Cost of customer waiting for service ii) Cost of service capacity. The cost of customer waiting include the Salaries paid to employees while they wait for services (machines waiting for tools, the driver of truck waiting to unload); any loss of business due to customer refusing to wait and possibly going elsewhere in future and the cost of space for waiting (fuel consumed by planes waiting to land). The cost of service capacity includes, the no of checkouts at a supermarkets , the no of repair people to handle equipment to breakdowns etc can be defined as the costs of maintaining the ability to produce service.
These two costs are inversely proportional to each others. Addition of more service centers (As capacity increase) will increase the service capacity and ultimately minimize the waiting line or waiting cost because the no. of customer waiting and the time they wait tend to decrease. However, additions of service facility would ultimately increase the cost of providing services. Similarly, if the no. of service center are reduced, it minimizes the service costs but increase the waiting costs. Thus the objective of quencing theory is to minimum the total cost associated with quenching system. The relation between these two costs is shown in figure below.
It is clear from the figure that an increase in the service facility (service center) will reduce the waiting line cost and increase the cost of providing service. Thus total cost, which is obtained by adding these two costs component together decrease up to a point and then rises as more and more service is provided. Thus the objective of the queuing theory is simply to determine the service level where the cost of system is lowest. This is the point where cost of service capacity line and waiting line cost cross each other. At this point, minimum total cost waiting line cost will equal to cost of providing minimum service. The Queuing System: - The queuing system consists essentially of three major components: i) The source population and way the customer arrive at the system. ii) The serving system
iii) How customer exists the system.
Customer arrive Waiting lineServer Exit
A. Customer arrive:- Arrivals at the system may be drawn from a finite or infinite population. A finite population refers to the limited no. of customer that will use the service. An example is a nurse may be responsible for answering patent calls for a 10-bed ward. In an infinite source situation, the potential no. of customers greatly exceeds system capacity. Examples are supermarkets, drug...