The Concepts and Application of the Queuing Model - Essay Example

Queuing Model

Introduction

Queuing model involves networks which are connected by different routes. The networks are represented by queue networks that can be represented using images. The main focus of studying the model is to obtain the equilibrium distribution of the networks. The model mainly involves a mathematical study of the waiting lines or queues. The model plays an essential role in the prediction of the queue lengths as well as the waiting times (Kingman, 2010). The model is also considered as part an important branch of operations research. The results obtained from the model are used for business decision making. This is mainly in terms of resources required to provide a service to the customers. It is for this reason that the model is increasingly becoming relevant for business organizations. The model is also an important measure of system performance in an organization. The utilization of the servers as well as the delays caused to the customers who are accessing a product or service can be determined through the use of the model. When dealing with simple systems, the computation is usually carried out mathematically (Harchol-Balter, 2012). However, when dealing with the complex systems, simulations may be required. The meaning as well as relationship of important performance measures can be obtained through the use of the model. The effects of varying inputs as well as parameters can be obtained through the use of the model. The paper thus discusses the concepts and application of the Queuing model.

Discussion

Main concepts

The model was first developed by a researcher known as Agner Krarup Erlang and it was mainly for the purposes of describing the telephone exchange in Copenhagen. However, the model has seen a wide range of application since then. The model is currently being used in different sectors including the telecommunication, engineering traffic and computing. The model is also used in the design of the coffee shops, offices, shops, banks and hospitals (Kingman, 2010). The model can be utilized through the use of different nodes with the common being the single queuing node. This node can be described through the use of the Kendall’s notation. The node operates through identifying and describing the time between arrivals at the queue, size of the job and the number of servers available at the nodes. The concepts of Markov chains are also applied in the queuing model. This is mainly used for the purposes of reducing the queues through the use of mathematical models. A common concept that is also utilized when using the model includes the M/D/K queue (Kingman, 2010). M stands for means Markov and it is used for the purposes of determining the arrivals based on the poison process. D stands for deterministic job arriving at the queue requiring a fixed amount of service. K stands for the number of servers at the queuing mode when there are more jobs that may not be handled immediately by the server or node. The Poisson process plays an important role in terms of developing the mathematical calculations.

Queuing nodes and scheduling policies

In most cases, the Poisson process has an exponentially distributed service requirements. This is used alongside the probability distribution concepts. The concepts of the model therefore require a lot of calculations and mathematical analysis. It is for this reason that the queuing model has become an important area of research for the mathematicians (Kingman, 2010). The mean waiting time at the queue has to be determined when the mathematical concepts are applied in the model. This can be obtained through the utilization of the matrix geometric method. However, one of the challenges that may be faced when using this method includes the performance metrics. Different scheduling policies can be utilized in the queuing nodes. The first in fist out principle is used when dealing with the queues. According to the principle, the customers are usually served one at a time with the customer who has been waiting for the longest period being served first (Harchol-Balter, 2012). The last in first out principle indicates that the customers are usually served one at a time. However, the customer with the shortest waiting time is revered first. This is unlike the first in first out principle where the customer with the longest waiting period is served first. The processor sharing requires that the service capacity is shared equally among the customers. It plays an important role in terms of ensuring that each customer at the queue is allocated an equal amount of time. The model is thus useful in ensuring that the problems associated with queuing and waiting time among the customers is reduced.

The model also indicates that priority can be used for serving the customers in a queue. This is an aspect that is usually applied by a high number of organizations. When prioritizing the needs of the customers, those with the highest priority are served first. The concepts of priority can be divided into two main types which include the non-preemptive and preemptive (Harchol-Balter, 2012). When dealing with the non-preemptive priority, the job in service cannot be interrupted. However, when dealing with the preemptive priority, a job in service can be interrupted. The model also recognizes the shortest job first principle. According to this principle, the next job to be served is the one with the smallest size. This is mainly aimed at ensuring that the shortest time possible is used to services. When the model is used by an organization, different types of service facilities can also be applied. The single server involves the customers lining up in order to be served by one facility. Parallel servers can also be used to attend to the customers in a queue and this involves customers lining up to be attended to by different servers (Harchol-Balter, 2012). This can be effective in terms of ensuring that a high number of customers are served. In a Tandem queue, there are many counters with several servers which where the customers can be served. This may in most cases is applied to facilities such as supermarkets and banks. The service facilities therefore play an essential role in ensuring that queues are managed.

Customer behavior

The customer behavior during the waiting time is an important aspect that needs to be considered. The model has highlights some of the behaviours that may affect the provision of services to the customers who are in a queue. Balking is one of the customer behaviors and it involves the failure to join the queue if it is too long (Kingman, 2010). Jockeying is a behavior that involves the customers switching between the queues with the belief that they will be served faster by doing so. Reneging is a behavior that involves the customers leaving the queues after waiting for too long without obtaining the required services. The queuing model indicates that a number of queues are connected by customer routing. The model indicates that there are different nodes and a customer can join another node or leave the once they have been served. Mathematical series can be used for indicating the actions that the customers can take after obtaining the service. The computations can be used to determine the number of customers in a network. Different equations are usually used in the model for the purposes of determining the nature of the queues and the tome taken to serve the customers (Kingman, 2010). A network algorithm has to be selected when using the model. The algorithm plays an essential role in ensuring that the service policy that gives the maximum throughput is selected. The characteristics of a network schedule can be determined through the use of the queuing algorithm.

Application of the workplace

Network modeling has a wide range of applications at the workplace. This is especially where customer has to physically visit the organization and queue so as obtain the services. The model is applied in the banking sector as well as other sectors in determining the average time that may be taken to provide the customers with the services. It is also useful in terms of estimating the waiting time for each of the customers based on the services that they require. During the process of determining the number of tellers in a bank, the queuing modeling is usually applied (Harchol-Balter, 2012). This is usually used for the purposes of estimating the approximate number of customers that may visit the bank. The average time required by the customers to obtain the service that they require is an important aspect that is usually considered. The duration taken by the customers and the expected number of customers is used during the calculation to determine the estimated waiting time for each of the customers. The waiting time is influenced by the nature of activities that the customers have to perform once they have reached the teller. The use of the model is an important aspect that has enabled the banking industry to improve on its efficiency during the delivery of services to the customers (Harchol-Balter, 2012). It is possible for the customers to know the average waiting time at the queue while obtaining the banking services. This has greatly reduced the incidences of jockeying and reneging which was common in the past.

The quality of services offered to the customers in the banking industry has greatly improved as a result of using the model. The banks usually encounter long queues on a daily basis. Thousands of customers are usually served by the banks and hence the long queues that are usually encountered. However, with the use of the model, it is possible for the customers to join the queues with full information of the time that they are likely to spend at the queue. This plays an important role in ensuring that the incidences of balking are reduced. Bottlenecks are also identified when the model is used and hence impacting positively on the quick delivery of services to the customers (Kingman, 2010). Customer satisfaction is an important aspect that contributes to the growth and development of the banks. Most of the customers are usually satisfied in the presence of efficiency when trying to obtain services from an organization. The model has also made it easy for the staff members at the bank to plan for their activities. This is because they are able to know the possible number of customers that they may handle during their shifts. This is an indication that the model is beneficial to the customers as well as the staff members. The current trend indicates that the model will continue finding more applications in the banking industry in future. Although technology is increasingly phasing out some of the activities that were once performed at the banks, queues will continue to be witnessed. The presence of the queues means that the model will continue to be relevant.

Conclusion

In conclusion, it is evident that the concepts and application of the queuing model is relevant to the modern day businesses. It is evident that the main concepts involve the use of mathematical information. Different processes have to be followed when using the model. It is evident that the model identifies the aspects that may influence the queues. The behavior of the customers is also considered in the model and it influences the decision making process. The model can be applied in different sectors including the banking industry. The use of the model impacts positively on the management of queues and customers in the banks. It is evident that the model will continue to be relevant in the sector in future.