Objective and Models of the Theory

Have you seen the lengthy queues before any institution, be it governmental or private? Have you wondered as to if there is any special factor associated with these queues? Well, the whole queuing theory and various models associated with this are attached to these queues.

This congestion of people arriving and queuing up for certain reasons before various offices and institutions, has a role to play in regards to OR benefit, which employs a number of queuing models to determine the actual scenario and compute certain data.

As per general definition, queuing theory can be said to be a mathematical computation of waiting lines or as they are called queues. With help of a model that is constructed in a queuing theory, lengths and waiting period can be calculated and further calculations in that theory is made in regards to that.

What does this system involve?

In this system there are a number of servers or facilities, known as call service channels which are primarily present to help people. Being of the single or multi-channel type, this system is specifically associated with communicating with people.

The centres associated with this regard happen to be work-stations, retailers, check-out counters and such other locations.

There are times when certain customers queue up in these service centres in a haphazard manner. Naturally this lack of a proper system results in them being served in a random manner which further creates a complete scenario of mismatch. Also, it may so happen that after a certain point of time that specific service counter is left empty by that concerned customer.

It is here that queuing system is required. This operative procedure is a random process where there are certain specific states and issues of time management. This status changes every time there is an activity that is happening, such as arrival of a prospective customer, completion of a particular service or waiting period of a customer before he decides to leave the queue.

Why is this queuing method important?

There is a deep connection that queuing system has with mathematical models. A relation is to be developed between specified operating conditions for the system and features associated with effectiveness measures having a value that can handle certain incoming demands.

There are certain measures that are taken against the objectives associated with this study:

• The mean of the number of customers who are served at per unit of time.
• Also, it is important to find out mean waiting time before customers are served and the expected number of customers.
• A check needs to be done regarding probability of people who could have been completely served within a stipulated time period.

The most important aspect that is determined with help of this study is presentation of a model format, where its perfect optimisation depends on parameters that have been chosen. While making this format, only simple queuing process is to be taken into consideration.

Characteristics associated with queuing systems:

 There are certain basic features that are common to every queuing system.

• The arrival process is to be noted with care. There are certain associated issues as pattern of arrival, timing associated with each arrival and various types of arrival are taken into consideration.
• A specific maintenance of queue discipline that includes factors as rules of conduct that is mandatory for every formation of queue.
• Also service mechanism needs to be taken into consideration. This includes, what is that duration of service that has been provided and what is this distribution of service with time consumed in rendering that service.

Mathematical Analysis:

In case of this queuing process, it is the Markovian theory that is used for better understanding and analysis of this process.

Markov’s process is defined as a random process which at any moment of time the probability of characteristics in future depends on state at a certain point of time and how that particular state was arrived at. Speaking in a simple manner, it is this mathematical association with Markov, where values may be proved for approximate handling of those aspects of queuing process which are specifically not distributed via the Poisson process. In most cases an approximate model is taken by various organisations in case they wish to make proper usage of this process.

Classification of systems:

In this domain, it is imperative to note that this system can be classified into certain formats before making complete usage of this technique. Here are the classifications:

• Loss and Delay system:

In this system of pure loss, it so happens that certain customers have to leave service centre without being attended because there is already a host of other people who are being served. Hence, this loss can be taken as a loss for the system itself.

A fine example can be seen in a telephonic centre, where due to all exchanges being busy, a particular person has to return back unattended. This comes down to be a loss for the whole system.

In system of delay, an arrival if not attended immediately takes refuge in the queue and waits until served. This has a wider usage in modern times, and can be put to test against various applications and theories.

Depending on the source type, there can be a classification made where models are divided into:

• Mite population size where consumers are few.
• Infinite population systems.

However, certain glitches can occur in regards to impatient clients.

Maintaining queue discipline:

In case of management of a queue there are multiple options as ‘’first come first serve’’, ‘’last come first serve’’, ‘’random selection techniques’’. In this case however, it is imperative that divisions be made in regards to priorities. Queues with higher priority should be attended before those with lower priority and that would help in correct monitoring of high arrivals. It may at times so happen that with arrival of high priority customers, service to lower priority clients should be stalled and vice-versa.

A fine example can be seen in the unloading of goods in dockyards. A discipline that is to be introduced is such that, when a ship that is unloading heavy products such as machinery sees arrival of a ship with perishable goods should immediately stop and attend to that. Since the ship with perishable goods cannot wait for a longer time period, hence it is imperative that being of higher priority, that should be attended first rather than the one with heavy industries.

There may arise a situation when the previously stalled lower priority client may be now attended and such a position in the queue is known as non-pre-emptive priority. An example set in this scenario may be something g like when a train is stuck midway and calls for an emergency entry into a particular platform, the permission can be given only to place that emergency train against the one that is already standing at the platform.

Understanding the various modes of queuing:

When service mechanism of this queuing is taken into consideration, it can be seen that customers at times leaves a certain queue and joins the next queue that is serving at a better rate. This mostly happens in those cases where service centres are placed in parallel mode or series. When operations are carried on in this specific series channel service mode, it is known as phases. However, it is not necessary for the arrival pattern to consistently correlate with other aspects that are part of this system.

Divisions of the system:

• Open system: In this case distribution of arrivals does not depend on status of the system, whether they are busy or free.
• Close system: The rate of arrival guides the other set of activities that are associated with it.

It is depending on these systems that total amount or people to be channelized depend and further actions take place.

Dual stand points:

This is extremely useful for determining position of the queues and service rendered by them.

• Owners of the queue specifically deal with depicting efficiency of that system and are concerned with loading the channels in the highest possible manner.
• The next favour is placed on customers, who would reduce their waiting time in the queue.

Thus, it can be stated that optimisation of this congestion process takes a detailed intrinsic understanding and evaluation, as well as assessment of all factors associated with it. Only when a detailed analysis is done can a final decision be taken that makes optimal usage of this technique.

It may so happen that customers may wish to increase optimal context of the servicing issue that may further lead to extra presence of service centres which though would increase the total costs accounted to these service centres with increase in number of channels.

In this case as per suggestion, it is the development of a singular system, keeping in mind the effectiveness of queuing problems that could only result in optimal usage of the available facilities and services.

Thus, it is important that one should study details associated with this queuing system and understand their needs rather than merely dealing with superficial aspects. This would help in better management of this system specifically.

Links of Previous Main Topic:-

• Duality in linear programming
• Learning objectives
• Learning objectives and chapter outline in assignment model
• Minimization problems
• Learning objectives the transportation problems
• Special case of traveling sales man problem
• Replacement theory learning objectives and chapter outline
• Learning objectives and chapter outline for waiting line queuing theory
• Objective and models of the theory
• Benefits and limitations of queuing theory
• Limitations of queuing theory
• Important terms used in queuing theory
• Types of queuing models
• Single channel queuing model

Links of Next Finance Topics:-

• Learning objectives and chapter outline for waiting line queuing theory
• Objective and models of the theory
• Benefits and limitations of queuing theory
• Limitations of queuing theory
• Important terms used in queuing theory
• Types of queuing models
• Single channel queuing model