Delay in Virtual-Circuit Networks
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In a virtual-circuit network, there is a one-time delay for setup and a one-time delay for teardown If resources are allocated during the setup phase, there is no wait time for individual packets Figure 816 shows the delay for a packet traveling through two switches in a virtual-circuit network The packet is traveling through two switches (routers) There are three transmission times (3T), three propagation times (3't), data transfer depicted by the sloping lines, a setup delay (which includes transmission and propagation in two directions),
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STRUCTURE OF A SWITCH
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Figure 816 Delay in a virtual-circuit network
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and a teardown delay (which includes transmission and propagation in one direction) We ignore the processing time in each switch The total delay time is
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Total delay = 3T + 3't + setup delay + teardown delay
Circuit-Switched Technology in WANs
As we will see in 18, virtual-circuit networks are used in switched WANs such as Frame Relay and ATM networks The data link layer of these technologies is well suited to the virtual-circuit technology
Switching at the data link layer in a switched WAN is normally implemented by using virtual-circuit techniques
STRUCTURE OF A SWITCH
We use switches in circuit-switched and packet-switched networks In this section, we discuss the structures of the switches used in each type of network
Structure of Circuit Switches
Circuit switching today can use either of two technologies: the space-division switch or the time-division switch
In space-division switching, the paths in the circuit are separated from one another spatially This technology was originally designed for use in analog networks but is used currently in both analog and digital networks It has evolved through a long history of many designs
Crossbar Switch A crossbar switch connects n inputs to m outputs in a grid, using electronic microswitches (transistors) at each crosspoint (see Figure 817) The major limitation of this design is the number of crosspoints required To connect n inputs to m outputs using a crossbar switch requires n x m crosspoints For example, to connect 1000 inputs to 1000 outputs requires a switch with 1,000,000 crosspoints A crossbar with this number of crosspoints is impractical Such a switch is also inefficient because statistics show that, in practice, fewer than 25 percent of the crosspoints are in use at any given time The rest are idle Figure 817
Crossbar switch with three inputs and four outputs
II III IV
Multistage Switch The solution to the limitations of the crossbar switch is the multistage switch, which combines crossbar switches in several (normally three) stages, as shown in Figure 818 In a single crossbar switch, only one row or column (one path) is active for any connection So we need N x N crosspoints If we can allow multiple paths inside the switch, we can decrease the number of crosspoints Each crosspoint in the middle stage can be accessed by multiple crosspoints in the first or third stage
n[ N n[ n[
Stage 1 Stage 2 Stage 3
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STRUCTURE OF A SWITCH
To design a three-stage switch, we follow these steps: 1 We divide the N input lines into groups, each of n lines For each group, we use one crossbar of size n x k, where k is the number of crossbars in the middle stage In other words, the first stage has N/n crossbars of n x k crosspoints 2 We use k crossbars, each of size (N/n) x (N/n) in the middle stage 3 We use N/n crossbars, each of size k x n at the third stage We can calculate the total number of crosspoints as follows:
N -en x k) + k (N x N) + -N(k x n) = 2kN + k (N)2 n n n n n
In a three-stage switch, the total number of crosspoints is
which is much smaller than the number of crosspoints in a single-stage switch (N2 )
Design a three-stage, 200 x 200 switch (N = 200) with k = 4 and n = 20
In the first stage we have N/n or 10 crossbars, each of size 20 x 4 In the second stage, we have 4 crossbars, each of size 10 x 10 In the third stage, we have 10 crossbars, each of size 4 x 20 The total number of crosspoints is 2kN + k(N/n)2, or 2000 crosspoints This is 5 percent of the number of crosspoints in a single-stage switch (200 x 200 = 40,000)
The multistage switch in Example 83 has one drawback-blocking during periods of heavy traffic: The whole idea of multistage switching is to share the crosspoints in the middle-stage crossbars Sharing can cause a lack of availability if the resources are limited and all users want a connection at the same time Blocking refers to times when one input cannot be connected to an output because there is no path available between them-all the possible intermediate switches are occupied In a single-stage switch, blocking does not occur because every combination of input and output has its own crosspoint; there is always a path (Cases in which two inputs are trying to contact the same output do not count That path is not blocked; the output is merely busy) In the multistage switch described in Example 83, however, only 4 of the first 20 inputs can use the switch at a time, only 4 of the second 20 inputs can use the switch at a time, and so on The small number of crossbars at the middle stage creates blocking In large systems, such as those having 10,000 inputs and outputs, the number of stages can be increased to cut down on the number of crosspoints required As the number of stages increases, however, possible blocking increases as well Many people have experienced blocking on public telephone systems in the wake of a natural disaster when the calls being made to check on or reassure relatives far outnumber the regular load of the system