# On Queuing Assignment

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In addition, we especially thanks to our honorable course instructor Dry. Abdul Hannah Aim, Professor Department of Management Information Systems (MIS), Faculty of Business Studies, University of Dacha We are privileged enjoying assistance and guidance of all the group members for supporting and giving pleasurable working experiences and helping each other prepare this assignment on “QUeUing Theory and The use of Queuing Theory of n Organization” from the beginning of our preparation.

Table of Contents Letter of Transmittal 1 Acknowledgement 2 Queuing Theory 4 Elements of waiting line analysis 5 The single server waiting line system 6-8 The Multiple Server Waiting line 9-10 Queuing in BBC (Best Fried Chicken) 11-15 Mathematical Model 16-21 Conclusion 27 Queuing Theory We have seen that as a system gets congested, the service delay in the system increases. A good understanding of the relationship between congestion and delay is essential for designing effective congestion control algorithms. Queuing Theory provides all the tools needed for this analysis. This article will focus on understanding the basics of this topic.

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Queuing analysis is a probabilistic from of analysis, not a deterministic technique. Thus the results of queuing analysis, referred to as operating characteristics, are probabilistic. These operating statistics (such as the average time a person must wait in the line to be served) are used by the manager of the operation containing the queue to make decision. Providing quick service is an important aspect of quality customer service. A number of different queuing model exist to deal with different queuing system. There are two common types of system – the single server system and the multiple server system.

Queuing Theory and Practice: A Source of Competitive Advantage Everyone has experienced waiting in line, whether at a fast-food restaurant, on the phone for technical help, at the doctor’s office or in the drive-through lane of a bank. Sometimes, it is a pleasant experience, but many times it can be extremely frustrating for both the customer and the store manager. Given the intensity of competition today, a customer waiting too long in line is potentially a lost customer. Understanding the nature of lines or “queues” and learning how to engage them is one of the most important areas in operations management.

QUeUes are basic to both external (customer-facing) and internal business processes, which include staffing, scheduling and inventory levels. For this reason, businesses often utilize queuing theory as a competitive advantage. Fortunately, Six Sigma professionals – through their knowledge of probability distributions, process mapping and basic process improvement techniques – can help organizations design and implement robust queuing models to create this competitive advantage. The Cost of Waiting in Line The problem in virtually every queuing situation is a trade-off decision.

The manager must weigh the added cost of providing more rapid service (i. E. , more checkout counters, more production staff) against the inherent cost of waiting. For example, if employees are spending their time manually entering data, a business manager or process improvement expert could compare the cost of investing in bar-code scanners against the benefits of increased productivity. Likewise, if customers are walking away disgusted because of insufficient customer support personnel, the business could compare the cost of hiring ore staff to the value of increased revenues and maintaining customer loyalty.

The relationship between service capacity and queuing cost can be expressed graphically (Figure 1). Initially, the cost of waiting in line is at a maximum when the organization is at minimal service capacity. As service capacity increases, there is a reduction in the number of customers in the line and in their wait times, which decreases queuing cost. The optimal total cost is found at the intersection between the service capacity and waiting line curves. Figure 1: Service Capacity vs.. Cost Source: Richard B. Chase and Nicholas J. Aquiline, Production and Operations Management, 1973, page 131.

Queuing Theory Queuing theory, the mathematical study of waiting in lines, is a branch of operations research because the results often are used when making business decisions about the resources needed to provide service. At its most basic level, queuing theory involves arrivals at a facility (i. E. , computer store, pharmacy, bank) and service requirements of that facility (i. E. , technicians, pharmacists, tellers). The number of arrivals generally fluctuates over the course of the hours that the facility is available for business (Figure 2).

Figure 2: Number of Arrivals at Facility Customers demand varying degrees of service, some of which can exceed normal capacity (Figure 3). The store manager or business owner can exercise some control over arrivals. For example, the simplest arrival-control mechanism is the posting of business hours. Other common techniques include lowering prices on typically slow days to balance customer traffic throughout the week and establishing appointments with specific times for customers. The point is that queues are within the control of the system management and design. Figure 3: Service Requirements

Queuing management consists of three major components: 1. How customers arrive 2. How customers are serviced 3. The condition of the customer exiting the system Arrivals: Arrivals are divided into two types: 1 . Constant – exactly the same time period between successive arrivals (i. E. , machine controlled). 2. Variable – random arrival distributions, which is a much more common form of arrival. A good rule of thumb to remember the two distributions is that time between arrivals is exponentially distributed and the numbers of arrivals per unit of time is Poisson distributed. The Servicing or

Queuing System: The servicing or queuing system consists of the line(s) and the available number of servers. Factors to consider include the line length, number of lines and the queue discipline. QUeUe discipline is the priority rule, or rules, for determining the order of service to customers in a waiting line. One of the most common used priority rules is “first come, first served” (OFFS). Others include a reservations first, treatment via triage (i. E. , emergency rooms of hospitals), highest-profit customer first, largest orders first, “best” customers first and longest wait-time first.

An important feature of the waiting structure is the time the customer spends with the server once the service has started. This is referred to as the service rate: the capacity of the server in numbers of units per time period (i. E. , 15 orders per hour). Another important aspect of the servicing system is the line structure. There are four types: single-channel/single-phase; single-channel/multi-phase; multi-channel/single-phase; and mufti-channel/ multi-phase. The simplest type of waiting line structure is the single-channel, single-phase. Here, there is only one channel for arriving customers and one hash of the service system.

An example is the drive-through window of a dry- cleaning store or bank. Exit: There are two possible outcomes after a customer is served. The customer is either satisfied or not satisfied and requires re-service. Waiting Line Models and Equations Table 1 shows the four types of commonly used waiting line models, along with key properties and examples. Table 1: Four Types of Waiting Line Models Model Layout Service Phase Source Population Arrival Pattern Queue Discipline Service Pattern Example Single channel Single Infinite Poisson OFFS Exponential Drive-through daydreamers 2 Multi-phase

Constant Automatic car wash (vacuum, wetting, washing, rinsing, drying window cleaning, parking) 3 Multi-channel Teller windows in a bank; multi-lane toll road 4 Finite Machine breakdown and repair in factory Some of the most basic questions a Six Sigma professional will want to ask when assessing and improving a business’s waiting line model include: Elements of waiting line analysis Waiting lines form because people or things arrive at the servicing function or, faster than they can be served.

However, this does not mean that the service operation is under- staffed or does not have the overall capacity handle the influx of customers. In fact , most businesses and organization have sufficient serving capacity available to handle their customers in the long run . Waiting line result because customer do not arrive at a constant ,evenly paced rate , nor are they all served in an equal amount of time . Operating characteristics are average values for characteristics that describe the performance of a waiting line system Decisions about waiting lines and the management of waiting lines are based on these averages for customer arrivals and service time . Different sets of formulas are used , depending on the type of waiting line system being investigated. For example, a bank drive -up teller window that has one bank clerk serving a single line of customer in cars is different from a single line of passengers at an airport ticket counter that is served three or four airline agents .

The single server waiting line system Component of a waiting line system include arrivals, servers, and the waiting line structure. A single server with a single waiting line is the simplest form of queuing system. As such, it will be used to demonstrate the fundamentals of a queuing system. As an example of this kind of system, consider Fast Shop Market. The most important facts to consider in analyzing queuing system such as the one in are the following: The queue discipline: The queue discipline is the order in which waiting customer are served.

The calling population: The calling population is the source of customers; it may be infinite or finite. The arrival rate: The arrival rate is the rate at which customers arrive at the service facility during a specified period of time. This rate can be estimated from empirical data derived from studying the system or a similar system, or it can be an average of these empirical data. The arrival rate is the frequency at which customers arrive at a tinting line according to a probability distribution. The arrival rate (Average number of arrivals per time period) The service rate: The service rate is the average number of customers who can be served during a time period p = The service rate (average number served per time period) Here, (customers are served at a faster rate than they arrive), we can state the following formulas for the operating characteristics of a single-server model: The probability that there are no customers in the system (all servers are idle) is: The average number of customers in the queuing system is:

The probability that n customers are in the queuing system is: The average number of customer spends in the queuing line system (waiting and being served) is: The average number of customers in the queue is: The average time a customer spends in the queue, waiting to be served is: The average time a customer spends waiting in the queue to be served is: The probability that a customer arriving in the system must wait for service (the probability that the server is busy) is: The probability that the server is idle: The Multiple Server Waiting line In multiple server-waiting lines two or more independent servers in parallel serve single waiting line. Here, = The arrival rate (Average number of arrivals per time period) p = The service rate (average number served per time period) c =The number of servers the mean effective service rate for the system, which must exceed the arrival rate.

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