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Loss networks ensure that sufficient resources are available when a call arrives. However, traditional loss network models for telephone networks cannot cope with today's heterogeneous demands, the central attribute of Asynchronous Transfer Mode (ATM) networks. This requires multiservice loss models.
This publication presents mathematical tools for the analysis, optimization and design of multiservice loss networks. These tools are relevant to modern broadband networks, including ATM networks. Addressed are networks with both fixed and alternative routing, and with discrete and continuous bandwidth requirements. Multiservice interconnection networks for switches and contiguous slot assignment for synchronous transfer mode are also presented.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Multiservice Loss Systems

Abstract
A loss system is a collection of resources to which calls, each with an associated holding time and class, arrive at random instances (see Figure 1.1). An arriving call either is admitted into the system or is blocked and lost; if the call is admitted, it remains in the system for the duration of its holding time. The admittance decision is based on the call’s class and the system’s state.
Keith W. Ross

Chapter 2. The Stochastic Knapsack

Abstract
The classical deterministic knapsack problem involves a knapsack of capacity C resource units and K classes of objects, with class-k objects having size b κ . Objects may be placed into the knapsack as long as the sum of their sizes does not exceed the knapsack capacity. A reward is r κ accrued whenever a class-k object is placed into the knapsack. The problem is to place the objects into the knapsack so as to maximize the total reward.
Keith W. Ross

Chapter 3. The Generalized Stochastic Knapsack

Abstract
In this chapter we again consider a stochastic system consisting of C resource units and K classes of objects. And we again suppose that class-k objects have size bκ and arrive and depart at random times. But we now permit the arrival and service rates to depend on the current knapsack state. In particular, with n and S defined as in the previous chapter, the time until the next class-k arrival is exponentially distributed with parameter λ κ (n) when the knapsack is in state n. Analogously, the time until the next class-k departure is exponentially distributed with parameter μ κ (n) when the knapsack is in state n. Clearly, μ κ (n) must satisfy μ κ (n) = 0 whenever n κ = 0. Note that the generalized stochastic knapsack becomes the stochastic knapsack, as studied in the previous chapter, if we set λ κ (n) = λ κ and μ κ (n) = n κ μ κ for all nS.
Keith W. Ross

Chapter 4. Admission Control

Abstract
Up to this point we have assumed that an arriving object is admitted into the knapsack whenever there is sufficient room. Such a policy is called complete sharing.
Keith W. Ross

Chapter 5. Product-Form Loss Networks

Abstract
A circuit-switched telephone network is depicted in Figure 5.1. It consists of a collection of switches and links, with each link containing a finite number of circuits. The links may use either analog or digital transmission.1 One or more adjacent links constitutes a route, and there may be more than one route joining a pair of switches.
Keith W. Ross

Chapter 6. Monte Carlo Summation for Product-Form Loss Networks

Abstract
We have repeatedly seen that performance measures for product-form loss networks take the form of simple functions of normalization constants. An effective method to calculate normalization constants therefore leads to an effective method to calculate performance measures. In Chapters 2 and 3 we presented efficient recursive and convolution algorithms to calculate normalization constants for stochastic knapsacks and generalized stochastic knapsacks. In Chapter 5 we presented efficient convolution algorithms for generalized tree and hierarchical tree networks. Nevertheless, calculating the normalization constant for arbitrary topologies is an NP-complete problem [102]. Many simple topologies — including the important star topology — appear to be particularly elusive for combinatorial approaches.
Keith W. Ross

Chapter 7. Dynamic Routing in Telephone Networks

Abstract
Up to this point, our loss networks have all had the following salient characteristic: An arriving call is admitted into the network if and only if there is sufficient bandwidth in each of the links along its predefined route. The models have conspicuously lacked alternative routes on which a call can be established when the predefined route is unavailable. Due to this absence of alternative routes, these loss networks are said to have fixed routing. Being simple to implement, fixed routing is employed in many regional and private circuit-switched networks. Moreover, it will be employed in many initial implementations of ATM.
Keith W. Ross

Chapter 8. Dynamic Routing in ATM Networks

Abstract
Given the great gains in performance achieved by dynamic routing for telephone networks, we are compelled to study similar routing schemes for ATM networks. Unlike traditional telephone networks, however, ATM networks statistically multiplex traffic with heterogeneous bandwidth and QoS requirements. The statistical multiplexing and the heterogeneity of traffic substantially complicate the design of the routing scheme.
Keith W. Ross

Chapter 9. Multiservice Interconnection Networks

Abstract
Up to this point we have ignored connection performance across the switches, focusing instead on connection blocking owing to the finite transmission resources. In this chapter we take a closer look at the connection performance of ATM switches.
Keith W. Ross

Backmatter

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