December 2 The equilibrium condition that the occupancy rate
In general, we do not like to wait.But reduction of the waiting time usually requires extra investments. To decide whether to invest, it is important to know the effect of the investment queue management on the waiting time. So we need models and techniques to analyst such situations. In this course we treat a number of elementary queueing models. Attention is paid to methods for the analysis of these models, and also to applications of queuing models. Important application areas of queueing models are production systems, transportation and stocking systems, communication systems and information processing systems. Queueing models are particularly useful for the design of these system in terms of layout, capacities and control. In these lectures our attention is restricted to models with one queue.
Models with more general service or interarrival time distributions
Situations with multiple queues are treated in the course “Networks of queues.” More advanced techniques for the exact, approximate and numerical analysis of queueing models are the subject of the course “Algorithmic methods in queueing theory.” The organization is as follows. Chapter first discusses a number of basic concepts and results from probability theory that we will use. The most simple interesting queueing model is treated in chapter, and its multi server version is treated in the next chapter. Models with more general service or interarrival time distributions are analysed in the chapters, and. Some simple variations on these models are discussed in chapter. Chapter is devoted to queueing models with priority rules. The last chapter discusses some insensitive systems. The text contains a lot of exercises and the reader is urged to try these exercises.
This is really necessary to acquire skills to model and analyst new situations.. Examples Below we briefly describe some situations in which queueing is important. Example.. Supermarket. How long do customers have to wait at the checkouts? What happens with the waiting time during peak-hours? Are there enough checkouts? Example.. Production system. A machine produces different types of products. What is the production lead time of an order? What is the reduction in the lead time when we have an extra machine? Should we assign priorities to the orders? Example.. Data communication. In computer communication networks such as the Internet data packets are transmitted over links from one switch to the next. In each switch incoming packets can be buffered when the incoming demand exceeds the link capacity. Once the buffer is full, incoming packets will be lost. What is the packet delay at queue management system price the switches? What is the fraction of packets that will be lost? What is a good size of the buffer? Example.. Parking lot. They are going to make a new parking lot in front of a super market Example..
Components necessary for queue management system
Assembly of printed circuit boards. Mounting vertical components on printed circuit boards is done in an assembly center consisting of a number of parallel insertion machines. Each machine has a magazine to store components. What is the production lead time of the printed circuit boards? How should the components necessary for the assembly of printed circuit boards be divided among the machines? Example.. Call centers of an insurance company. Questions by phone, regarding insurance conditions, are handled by a call center. This call center has a team structure, where each team helps customers from a specific region only. How long queue management system price do customers have to wait before an operator becomes available? Is the number of incoming telephone lines enough? Are there enough operators? Pooling teams? Example..
Toll booths. Motorists have to pay toll in order to queue management system pass a bridge. Are there enough toll booths? Example.. Traffic lights. How do we have to regulate traffic lights such that the waiting times are acceptable? Example.. Hospital emergency department. In a hospital emergency department patients arrive with various kinds of injuries and medical issues that require urgent treatment. How many nurses and doctors need to be on staff to provide patients with proper care in a timely manner? How many intensive care units are needed to hospitalize patients? Example.. Mobile communication network. Users download documents, visit websites and watch video clips on their laptops, tablets and smartphones. Should the data delivery for certain types of applications receive priority see more over others? How many access points need to be installed and where in order to ensure speedy data transfer? Performance measures Relevant performance measures in the analysis of queueing models are:The distribution of the waiting time and the sojourn time of a customer.