12 Introduction and Layered Network Architecture Chap.1 other reason,which will be more clear later,is that very long messages,which will be prevalent with ISDN.are probably better treated in the subnet as flows than as point arrivals. To put this question of modeling message arrivals for a session in a more pragmatic way,note that networks,particularly wide area networks built around a subnet as in Fig.1.3,generally handle multiple applications.Since the design and implementation of a subnet is a time-consuming process,and since applications are rapidly changing and expanding,subnets must be designed to handle a wide variety of applications,some of which are unknown and most of which are subject to change.Any complex model of message arrivals for sessions is likely to be invalid by the time the network is used.This point of view,that subnets must be designed to work independently of the fine details of applications.is discussed further in Section 1.3. At this point we have a conceptual view,or model,of the function of a subnet. It will provide communication for a slowly varying set of sessions:within each session, messages of some random length distribution arrive at random times according to some random process.Since we will largely ignore the interaction between the two directions of message flow for a session.we shall usually model a two-way session as two one-way sessions,one corresponding to the message flow in one direction and the other in the opposite direction.In what follows we use the word session for such one-way sessions. In matters such as session initiation and end-to-end acknowledgment,distinctions are made between two-way and one-way sessions. In principle a session could involve messages between more than two users.For example,one user could broadcast a sequence of messages to each of some set of other users,or the messages of each user in the set could be broadcast to each of the other users.Such sessions might become important in the future,especially for broadband ISDN.with applications such as video conferencing and television broadcast.We will not discuss such applications in any detail.but instead will simply model multiuser sessions as a multiplicity of one-way two-user sessions. Although the detailed characteristics of different kinds of applications will not be examined,there are some gross characteristics of sessions that must be kept in mind. The most important are listed: 1.Message arrival rate and variability of arrivals.Typical arrival rates for sessions vary from zero to more than enough to saturate the network.Simple models for the variability of arrivals include Poisson arrivals.deterministic arrivals (i.e.,a fixed time interval from each message to the next message),and uniformly dis- tributed arrivals (i.e.,the time interval between successive messages has a uniform probability density between some minimum and maximum interval). 2.Session holding time.Sometimes (as with electronic mail)a session is initiated for a single message.Other sessions last for a working day or even permanently. 3.Expected message length and length distribution.Typical message lengths vary roughly from a few bits to 10 bits,with file transfer applications at the high end and interactive sessions from a terminal to a computer at the low end.Simple models for length distribution include an exponentially decaying probability density,a uniform12 Introduction and Layered Network Architecture Chap. 1 other reason, which will be more clear later, is that very long messages, which will be prevalent with ISDN. are probably better treated in the subnet as flows than as point arrivals. To put this question of modeling message arrivals for a session in a more pragmatic way, note that networks, particularly wide area networks built around a subnet as in Fig. 1.3, generally handle multiple applications. Since the design and implementation of a subnet is a time-consuming process, and since applications are rapidly changing and expanding, subnets must be designed to handle a wide variety of applications, some of which are unknown and most of which are subject to change. Any complex model of message arrivals for sessions is likely to be invalid by the time the network is used. This point of view, that subnets must be designed to work independently of the fine details of applications, is discussed further in Section 1.3. At this point we have a conceptual view, or model, of the function of a subnet. It will provide communication for a slowly varying set of sessions; within each session, messages of some random length distribution arrive at random times according to some random process. Since we will largely ignore the interaction between the two directions of message flow for a session, we shall usually model a two-way session as two one-way sessions, one corresponding to the message flow in one direction and the other in the opposite direction. In what follows we use the word session for such one-way sessions. In matters such as session initiation and end-to-end acknowledgment, distinctions are made between two-way and one-way sessions. In principle a session could involve messages between more than two users. For example, one user could broadcast a sequence of messages to each of some set of other users, or the messages of each user in the set could be broadcast to each of the other users. Such sessions might become important in the future, especially for broadband ISDN, with applications such as video conferencing and television broadcast. We will not discuss such applications in any detail, but instead will simply model multiuser sessions as a multiplicity of one-way two-user sessions. Although the detailed characteristics of different kinds of applications will not be examined, there are some gross characteristics of sessions that must be kept in mind. The most important are listed: 1. Message arriml rate and mriahility of arrimls. Typical arrival rates for sessions vary from zero to more than enough to saturate the network. Simple models for the variability of arrivals include Poisson arrivals, deterministic arrivals (i.e., a fixed time interval from each message to the next message), and uniformly dis￾tributed arrivals (i.e., the time interval between successive messages has a uniform probability density between some minimum and maximum interval). 2. Session holding time. Sometimes (as with electronic mail) a session is initiated for a single message. Other sessions last for a working day or even permanently. 3. Expected message length and length distrihution. Typical message lengths vary roughly from a few bits to 109 bits, with file transfer applications at the high end and interactive sessions from a terminal to a computer at the low end. Simple models for length distribution include an exponentially decaying probability density, a uniform