Section 14.8. Exercises

14.8. Exercises

3.

1.	Consider a crossbar switching network similar to the one shown in Figure 14.4 but of size 8 x 8. Suppose that the crosstalk suppression of each 2 x 2 switch element is 40 dB. Calculate the maximum and minimum overall cross-talk suppressions for the crossbar switch. Calculate the average of overall cross-talk suppressions, using all possible existing paths.
2.	Consider the Spanke-Bene network shown in Figure 14.5. Suppose that the crosstalk suppression of each 2 x 2 switch element is 40 dB. Calculate the overall cross-talk suppressions, using all possible existing paths.
To design an 8 x 8 optical router, we are comparing three different structures, each using, respectively, a crossbar switching network, a Spanke-Bene network, and an 8 x 8 directional coupler. Which structure offers the best overall cross-talk suppression? Which structure has the lowest overall average switching delay?
4.	Consider a ring optical backbone network consisting of eight 2 x 2 switching nodes labeled 1 through 8. Nodes are interconnected with two fiber- optic rings carrying traffic in opposite directions. Three wavelengths , 1 , 2 , and 3 , are available on each link. A SONET network consisting of duplex lightpaths 2-4, 4-7, and 3-6 is constructed over this backbone. For convenience, assume that both halves of the duplex SONET network are identical in terms of wavelengths. Find the minimum number of wavelengths to construct the SONET network. Now, assume that another SONET network, consisting of duplex lightpaths 2-5, 5-6, and 2-8, is constructed over this backbone. Using the same assumptions as in part (a), find the minimum number of wavelengths to construct this SONET network. Both SONET networks are supposed to be constructed over this backbone network simultaneously . Find the minimum number of wavelengths to construct the two SONET networks.
5.	Suppose that four wavelengths exist on each single link of a three-link path . For each lightpath request, the first available wavelength is assigned. The wavelength request arrival is assumed to be Poisson, with the rate that leads to 80 percent utilization. For each lightpath, the probability that a wavelength is used on a link is 20 percent. Assume that a lightpath request chooses a route with two links. Find the blocking probability on this link. Find the probability that a given wavelength is not free on at least one of existing two links of a route. Find the probability that a lightpath request is blocked.
6.	Consider an optical network with n nodes. Let L i,j be an arriving Poisson traffic rate on link i , j in packets per second, and let 1 / i,j be the mean time of exponentially distributed packet transmission on link i , j . Find the average queueing delay on link i , j . Let s i,j be the number of source/destination pairs whose traffic is routed over link i , j . In this case, find the average queueing delay on link i , j . Find the average queueing delay for a packet, given all source/destination pairs.