Queuing Theory

Posted on Jun 21 2019 - 11:35pm by simplinotesadmin

Queuing Decision Theory

Queuing theory was developed in the early 1900s by A.K. Erlang to study fluctuating demands in telephone traffic. After World War II, Erlang’s work was extended to general business applications, and today it is used extensively in both materials and customer processing operations.

Features of Queuing System

1. Length of the Queue
It indicates the average number of customers waiting in the line. Large queues indicate poor server and small queue imply too much server capacity.

2. System
System means maximum capacity of the queue.
System = Customer waiting + Customer being served

3. Waiting Time
This is the average time that a customer has to wait to get service. If waiting time is too much long , it may result in potential loss of revenue and set back to the goodwill of the business.

4. Total time
Total time means time taken from entry in the queue to completion of service.

5. Idle time
The relative frequency for which service system remain idle. Idle time leads to increase in the related cost.

6. Arrival Pattern
The pattern of arrival of customers at service station is known as arrival pattern of queue. When arrival rate is random, the customers arrive in no logical pattern or order over time. This represents most cases in the business world. When arrivals are random, we have to know the probability distribution describing arrivals, specifically the time between arrivals. Management scientists have demonstrated that random arrivals are often best described by the Poisson distribution.

7. Service Pattern
Although arrival pattern is random in most situations and can be satisfactory modeled by using the Poisson distribution, , service pattern exhibits no obvious or consistent pattern. However for the sake of simplicity, and in order to reduce the necessity of complex mathematically models, simple queue theory assumes that service pattern can be represented by treating them as being exponential.

8. Service Management
For producing service to the incoming customers at the Service Station certain service points are established. The number of these service points mostly depends upon the number of customers, rate of arrivals time taken for providing service to a single customer, availability of persons/resources for producing service etc. depending upon these variables, a customer service channel can be either a single channel or a multi channel.

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