Queuing Theory

The word ‘queue’ is not unfamiliar to us. We have all stood in a queue for railways reservations, or airline tickets, in a ration shop, or for water from a municipal tanker. Just as people wait for these services, materials wait at a work center to be worked on and papers wait at a section in an office to be processed. Queuing theory tries to analyze why such waiting lines occur and what solutions can be offered to improve the desired performance.

A number of solutions can be evolved to have almost zero waiting time like,

* There be one, or two, or three clerks at a counter
* Jobs waiting at a work center can be taken up for processing in the order they arrive, or in accordance with their increasing processing times, or in accordance with their due dates
* The latter alternatives make such difference
* A service system can be thought of to avoid making housewives wait for long, for a rationed supply of kerosene
* The number of maintenance mechanics so that too many machines, which have broken down, are not kept waiting for repair thus holding up productive work for long

Queuing theory attempts to evolve solutions to the above alternatives.

Queuing System has the following three features,

(a) Commuters arriving to buy railway tickets
(b) Parts arriving to be assembled in an Assembly department.
(c) Invoices arriving at an order desk.

The characteristics of the waiting line depend on the characteristics of the arrival process. Arrivals could be single or bunched; controlled or uncontrolled. Occasions, where the arrival process is almost under control, may be called ‘deterministic’ while occasions where there is no absolute control may be called ‘probabilistic’.

Arrivals could be state-dependent or independent. For example, a long time of queue may either discourage or encourage people to join the queue. Even with materials and machines, there could be a system-dependence on the part of the arrivals. Thus ‘arrivals’ may depend upon the characteristics of preceding ‘arrivals’ and/or the servicing characteristics and/or the servicing characteristics and/or the result of that is the waiting line characteristics.


Examples of service are as follows:

(a) The number of commuters that a railway ticket counter clerk attends to.
(b) The number of parts assembled in an Assembly Shop.
(c) The number of breakdowns that are repaired in a Maintenance Shop.
(d) The number of orders or invoices processed by order clerk.

The characteristics of the waiting line depend also upon the characteristics of the services offered. It may be important to analyze:

(a) Whether the service time or service rates as mentioned above, are constant or are probabilistic?
(b) Whether service-rates are dependent upon the queue system itself? For instance, does a Barber consciously increase his speed looking at the number of people waiting for his services on a Sunday morning?

Queuing Discipline:

This is a rule or a set of rules which describes the order in which the arrivals will be serviced, for example:

(a) First come first served.
(b) Serve the shortest duration next; this means that you service the operation the shortest time first, next shortest second, and so on. For instance a barber trims the moustache first, shaves next, and does the hair cut job thereafter.
(c) When there are more than ten commuters waiting in a queue at the booking office, open another counter for issuing tickets.
(d) Serve the last arrival first.
(e) Serve the job taking the longest amount of time first, and proceed to the next longest job.
(f) Serve each unit in the queue system partially. Like barbers who attend partially to one customer and then move on to the second, thereby keeping all customers waiting. Many manufacturing systems behave on similar lines.
(g) Serve the jobs that are intrinsically high priority jobs by stopping work on lower priority jobs. If an order from a prestigious firm arrives give it a preference over all others even those in process and take it up immediately for manufacture.

Thus, Queue discipline is basically the priorities scheme operating in the servicing of the units in a system.

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