Problems in .NET Printing Code 128 Code Set C in .NET Problems

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9.1 9.2 Explain, in your own words, and distinguish between, the terms cell dwell time, call holding time, and channel holding time.

(a) The probability distributions of the channel holding time, the cell dwell time, and the call-holding time (call length) are related by (9.2). Show for the case of exponentially distributed dwell time and call holding time that the channel holding time is exponential as well, with the average channel holding time related to the averages of the other two times by (9.

3). (b) Verify that the probability Ph of a handoff in the case of exponentially distributed random variables as in (a) is given by (9.4).

(c) Verify and discuss the results for the three examples of different cell sizes and mobile speeds given following (9.5a). Choose some other examples and calculate the same three parameters, average time between handoff, probability of a handoff, and average channel holding time, for each example.

. Performance analysis Using Fig. 9.1, show h .

NET Code 128 Code Set A ow the ow-balance equation (9.6) is derived. Where is the assumption of exponentially distributed random variables used in deriving this expression (See problem 9.

6(a) below.) Consider the discussion in the text of the guard-channel admission-control procedure. (a) Using the concept of local-balance as applied to Fig.

9.3, verify the expressions for the probabilities of state p1 and p2 given by (9.10) and (9.

12) respectively. Show the general expressions for the probability of state in the two regions indicated in Fig. 9.

3 are given by (9.13) and (9.14).

(b) Show the handoff dropping and new-call blocking probabilities are given, respectively, by (9.16) and (9.17).

(c) Table 9.1 shows the results of iterating (9.16) and (9.

17), as explained in the text, to nd the handoff dropping and new-call blocking probabilities for the two examples of a macrocellular system and a microcellular system. A macrocell in these examples has a radius of 10 km, a microcell has a radius of 100 m. Mobile speeds are taken to be 60 km/sec in the macrocellular case, 5 km/sec in the microcellular case.

The number of channels available in either case is m = 10. Carry out the iteration indicated for each system, starting with the two probabilities set to 0, for the case of, rst, g = one guard channel, and then two guard channels. Do this for a number of values of new-call arrival rate, as indicated in Table 9.

1. Verify and discuss the appropriate entries of Table 9.1.

Show, in particular, how the introduction of the guard channels reduces the handoff dropping probability at the expense of some increase in blocking probability. (d) Repeat the calculations of (c) for the other examples used in 9.2(c).

(a) Show the Erlang-B formula for the probability of blocking is given by (9.18). (b) Plot the Erlang-B blocking probability versus (or A, in Erlangs, as de ned in 3) for m = 1, 5, 10, and 20 channels.

(c) A useful recursive relation for calculating the Erlang-B blocking probability of (9.18) is given as follows 1 m =1+ , PB (m) PB (m 1) PB (0) = 1. Derive this relation a nd use it to calculate and plot PB (m) for 1 m 20 and 1 20 Erlangs. 9.6 This problem relates to the handoff of calls for which the cell dwell time is non-exponential.

(a) Why should there, in general, be different cell dwell times, one for newly generated calls, the other for calls handed off from another cell (Hint: Where, in a cell, can a new call be generated Where is a handoff call, newly arriving at a cell, generated ) Why does the memoryless property of the exponential distribution result in a single dwell-time distribution (b) Use Fig. 9.1 and the de nition of the two types of handoff probabilities, PN for newly arriving calls and PH for calls handed over from another cell, to derive the.

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