Basic Elements of Queuing Model

The success of this queuing model specifically depends on certain basic elements, a correct denomination of which is important for clear understanding of the concept. While considering the elements, it is important to note that there are certain specific factors which are associated with this basic element of the queuing model.

A clear understanding of those factors is important to ensure that students do not get diverted while dealing with this particular topic.

Factors associated with elements of the queuing model:

It is based on these factors that further elements are to be understood. Once these details are clarified, certain analytical decisions can be taken and it is based on those decisions that final allocation of resources is to be done.

• Total number of customers:

There are 2 systems that need to be considered in this format: Open system and Closed system. In case of a closed system, there is a limited number of people that are associated with any particular job, or people those have to be served. There is a single machine, or individual to deal with this issue.

In case of unlimited systems, this whole process includes multiple clients at a single time, and they have to be served.

• The arrival of people:

This is one random note that is taken into consideration. The manner in which people arrive are random, and between adjacent intervals as well, there are certain random arrivals. This arrival may be in a single set or even a bulk and therefore has to be counted in terms ofprobability distribution. This system is also known as arrival pattern.

• Formation of the queue for getting a service:

The number of people that are taken into consideration when they are standing in a line waiting to be served is known as forming of a queue. This process of waiting to be served is known as queuing up.

There are 2 important aspects of queue that includes: Queuing discipline and Maximum size.

Maximum size implies a total number of customers who are waiting in the queue to be served.

Queuing discipline has certain features associated with it, and can be defined as the manner in which a queue is organized.

• Priority queue is that where people having priority regarding getting their service is allowed. In this case, given that every individual is prioritized, those with a lower priority get served later than those with a higher priority.
• Serve in random order (SIRO) implies that category in which people come in haphazardly asking for service, and they are provided service in that manner
• Last come first out (LIFO) implies that system where people who come in at the last moment are also served in the best manner and first-hand.
• First in first out (FIFO) is that usual technique that is followed which ensures those customers who have come first should be served on a first-hand basis.

There is another facet where customers can join into any queue, and they have a source in an infinite set.

Also, in this queuing system, peculiar human behavior has been noticed.

When any person after waiting in queue loses his patience, he leaves that queue, and it is called reneging.

When people from a larger queue join into a smaller queue, it is known as jockeying.

Also, if people do not decide to enter any queue due to their personal reasons, it is known as balking.

• Providing of service:

This is that time which is taken as period for which customers had to wait before getting the final service. This could both include that period, for which they had to wait as well as period when they were being served. It is also taken as a random rather than having any specified system.

• Output that is provided:

This is taken to be the mode in which clients leave a particular system after they have been served. Though in most cases, it is ignored, however in certain cases there is the process of ‘round-robin’ facility where served customers again enter the system to get served for some other process.

Once these factors are well understood, and complete analysis is made in regards to them, it can be found that how many resources are to be allocated to every party and what would be the result of that.

Explaining the queuing theory:

This theory is said to be a collection of mathematical models that are required for representing the various types of queuing system, which have the capacity to take in input parameters and provide quantitative parameters which on the whole helps in getting an ideal and systematic view of this whole system.

Since, this is a system that is specifically based on assumptions, and the processes are random in nature, so the systems cannot be termed as soluble, and for them, simulation technique is to be applied.

Also, there are other constraints that need to be understood as parity between the costs that are associated with providing of service, as well as costs associated with waiting for that particular service and returning without getting it. In such a scenario, it can be seen that the costs keep increasing, as people who have not been served on a single day have a tendency to come back the next day to be served again. In this way, there is an additional cost since money is spent on that same person.

In case of high-quality service that is provided by most of the services in present times, total costs associated are comparatively higher, but individual costs against people who are waiting in the queue are reduced comparatively, allowing greater profit and ensuring correct resource allocation.

Hence, it is important that for correct utilization of resources, an optimum system of configuration is to be found, and simulation theory is to be applied.

Thus, it can be stated that with a correct queuing theory, resource allocation can be done in the best way resulting in increasing profits of any business institution.

Links of Previous Main Topic:-

• Introduction to statistics
• Knowledge of central tendency or location
• Definition of dispersion
• Moments
• Bivariate distribution
• Theorem of total probability addition theorem
• Random variable
• Binomial distribution
• What is sampling
• Estimation
• Statistical hypothesis and related terms
• Analysis of variance introduction
• Definition of stochastic process
• Introduction operations research
• Introduction and mathematical formulation in transportation problems
• Introduction and mathematical formulation
• Queuing theory introduction

Links of Next Statistics Topics:-

• Kendalls notation
• Queuing models based on birth and death processes
• Mm1 fifon model
• Mms fifo model
• Mms fifon 5 model
• Non poisson queuing models
• Inventory control introduction
• Simulation introduction
• Time calculations in network
• Introduction of game theory