Introduction to IP and ATM Design Performance - Part 3

Chương 7 và 8, chúng tôi điều tra hành vi xếp hàng cơ bản tìm thấyATM bộ đệm đầu ra. Xếp hàng này phát sinh vì nhiều dòngtế bào được ghép lại với nhau, vì vậy nhu cầu (tương đối ngắn)bộ đệm. Chúng tôi đã phát triển phương trình cân bằng trạng thái của hệ thốngkết thúc của bất kỳ khe thời gian, từ đó chúng ta có nguồn gốc mất di động và kết quả chậm trễ.Chúng tôi cũng xem xét xấp xỉ nặng, giao thông: phương trình rõ ràngcó thể được sắp xếp lại nhằm sản xuất ra...
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Introduction to IP and ATM Design Performance - Part 3 Introduction to IP and ATM Design Performance: With Applications Analysis Software, Second Edition. J M Pitts, J A Schormans Copyright © 2000 John Wiley & Sons Ltd ISBNs: 0-471-49187-X (Hardback); 0-470-84166-4 (Electronic)PART IIIIP Performance andTraffic Management Introduction to IP and ATM Design Performance: With Applications Analysis Software, Second Edition. J M Pitts, J A Schormans Copyright © 2000 John Wiley & Sons Ltd ISBNs: 0-471-49187-X (Hardback); 0-470-84166-4 (Electronic)14 Basic Packet Queueing the long and short of itTHE QUEUEING BEHAVIOUR OF PACKETS IN AN IP ROUTERBUFFER In Chapters 7 and 8, we investigated the basic queueing behaviour found in ATM output buffers. This queueing arises because multiple streams of cells are being multiplexed together; hence the need for (relatively short) buffers. We developed balance equations for the state of the system at the end of any time slot, from which we derived cell loss and delay results. We also looked at heavy-traffic approximations: explicit equations which could be rearranged to yield expressions for buffer dimensioning and admission control, as well as performance evaluation. In essence, packet queueing is very similar. An IP router forwards arriving packets from input port to output port: the queueing behaviour arises because multiple streams of packets (from different input ports) are being multiplexed together (over the same output port). However, a key difference is that packets do not all have the same length. The minimum header size in IPv4 is 20 octets, and in IPv6, it is 40 octets; the maximum packet size depends on the specific sub-network technology (e.g. 1500 octets in Ethernet, and 1000 octets is common in X.25 networks). This difference has a direct impact on the service time; to take this into account we need a probabilistic (rather than deterministic) model of service, and a different approach to the queueing analysis. As before, there are three different types of behaviour in which we are interested: the state probabilities, by which we mean the proportion of time that ž a queue is found to be in a particular state (being in state k means the queue contains k packets at the time at which it is inspected, and measu- red over a very long period of time, i.e. the steady-state probabilities);230 BASIC PACKET QUEUEING the packet loss probability, by which we mean the proportion of ž packets lost over a very long period of time; the packet waiting-time probabilities, by which we mean the proba- ž bilities associated with a packet being delayed k time units. It turns out that accurate evaluation of the state probabilities is paramount in calculating the waiting times and loss too, and for this reason we focus on finding accurate and simple-to-use formulas for state probabilities.BALANCE EQUATIONS FOR PACKET BUFFERING:THE GEO/GEO/1 To analyse these different types of behaviour, we are going to start by following the approach developed in Chapter 7, initially for a very simple queue model called the Geo/Geo/1, which is the discrete-time version of the ‘classical’ queue model M/M/1. One way in which this model differs from that of Chapter 7 is that the fundamental time unit is reduced from a cell service time to the time to transmit an octet (byte), Toct . Thus we have a ‘conveyor belt’ of octets – the transmission of each octet of a packet is synchronized to the start of transmission of the previous octet. Using this model assumes a geometric distribution as a first attempt at variable packet sizes: k1 b k D Prfpacket size is k octetsg D 1 q Ðq where q D Prfa packet completes service at the end of an octet slotg We use a Bernoulli process for the packet arrivals, i.e. a geometrically distributed number of slots between arrivals (the first Geo in Geo/Geo/1): p D Prfa packet arrives in an octet slotg Thus we have an independent and identically distributed batch of k octets (k D 0, 1, 2, . . .) arriving in each octet slot: ...