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Hiệu suất của hệ thống thông tin máy tính P8

IN this chapter numerical the class of PHlPH however, as special cases of GIGI 1 queues; due to the specific methods efficient solution. known as matrix-geometric is not to present solution. efficient organised Instead, solution insight The aim of this chapter and their matrix-geometric geometric models, queueing methods, together models. is further with their all the known operation, material our aim is to show the usefulness and to show that techniques, are a good alternative 8.1 we readdress to provide into their This chapter matrix-geometric play an important. | Performance of Computer Communication Systems A Model-Based Approach. Boudewijn R. Haverkort Copyright 1998 John Wiley Sons Ltd ISBNs 0-471-97228-2 Hardback 0-470-84192-3 Electronic Chapter 8 PH PH 1 queueing models IN this chapter we address the class of PH PH 1 queues. These queues can be seen as special cases of G G 1 queues however due to the specific distributions involved efficient numerical algorithms known as matrix-geometric methods can be applied for their solution. The aim of this chapter is not to present all the known material on PH PH 1 queues and their matrix-geometric solution. Instead our aim is to show the usefulness of matrixgeometric methods to provide insight into their operation and to show that PH PH 1 models together with their efficient solution techniques are a good alternative to G G 1 queueing models. This chapter is further organised as follows. In Section 8.1 we readdress the analysis of the M M 1 queue in a matrix-geometric way . This is used as an introduction to the matrix-geometric analysis of the PH PH 1 queue in Section 8.2. Numerical algorithms that play an important role in the matrix-geometric technique are discussed in Section 8.3. We then discuss a few special cases in Section 8.4. In Section 8.5 we discuss the caudal curve which plays an interesting role when studying the tail behaviour of queues. We finally comment on additional queueing models that still allow for a matrix-geometric solution in Section 8.6. 8.1 The M M 1 queue Consider an M M 1 queueing model with arrival rate A and service rate p . The Markov chain underlying this queueing model is a simple birth-death process where the state variable denotes the total number of packets in the queueing station. Since the state variable is a scalar such a process is sometimes called a scalar state process. The generator matrix 146 8 PH PH 1 queueing models Figure 8.1 The state-transition diagram for the M M 1 queue Q of the CTMC underlying the M M 1 queue has the .