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MB0048 : What do you understand by (i) Queue discipline, (ii) Arrival process (iii) Service process?

Posted on: October 5, 2011

MB0048 : What do you understand by (i) Queue discipline, (ii) Arrival process (iii) Service process?
Answer: – Queue discipline

The pattern of selection for service from the pool of customers is of two types. The common pattern is to select in the order in which the customers arrive. “First come first served” is a common example. In issuing materials from a store’s inventory sometimes the storekeeper follows the “Last in First Out” principle because of the convenience it offers for removal from stocks and handling.

There are queues according to priority to certain types of customers. This type of queuing can have two approaches: non pre-emptive and pre-emptive. In case of non pre-emptive priority, the customer getting service is allowed to continue with service till completion, even if a “priority customer” arrives midway during his service. This is a common form of priority. Pre-emptive priority involves stopping the service of the non priority customers as soon as the priority customer arrives.

Priority given to repairs of a production holding machine over an auxiliary unit for allocation of maintenance labor force is a typical example. Preference is given to larger ships over the smaller ones irrespective of the order in which they arrive for allocation of berths.

Arrival process

The arrival of customers can be regular as in case of an appointment system of a doctor or flow of components on a conveyor belt. The regular pattern of arrivals is neither very common nor very easy to deal with mathematically. Our primary concern is the pattern of completely random arrivals.

If the number of potential customers is infinitely large, then probability of an arrival in the next interval of time will not depend upon the number of customers already in the system. (The assumption is valid by and large, except for queues involving a small finite number of customers.) When the arrivals are completely random, they follow the Poisson distribution, which equals to the average number of arrivals per unit time.

Sometimes it is necessary to distinguish between groups of customers, such as male and female callers, or large and small aircrafts during the arrivals. There are several other types of arrival patterns which shall not be dealt with due to their restricted applications.


Service process

Service Facility or Service process is based on three parameters – Availability of Service, Number of Service Centres and Duration of Service.

i) Availability of service

It is necessary to examine if there are any constraints that reduce the number of customers to be served at a time, apart from specifying the time span of the availability of service. For example, in a waiting line for a suburban train, apart from the timings of the train services, the probability distribution of the number of passengers that can be accommodated in a train that arrives is relevant.

ii) Number of service centres

If only one service centre is referred to as a service channel, obviously only one customer can be served at a time. There will definitely be more than one service centre and the behaviour of the queues will vary with the number of channels available for service. Multiple service channels may be arranged in series or in parallel.

Multiple service channels are arranged in series when a customer has to go through several counters one after another with each providing a different part of the service. For instance, bank counters where a customer has to go to at least two counters to withdraw is an example of arrangement in series.

On the other hand ticket booths in a railway station have multiple channels with parallel arrangement.

iii) Duration of service

This is the length of time taken to serve a customer. This can be constant or varying.

(a) Constant service time: Though not in practice, an assumption that service time is constant holds true, if the pattern of arrivals is very irregular.

(b) Completely random service time: The service time can be considered completely random when:

· The server does not distinguish between the various arrivals

· The server does not deliberately change the duration of service on the basis of the time taken to serve the previous arrival.

· The server forgets the time for which he has been serving a customer.


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