Mobile Wireless Communications in .NET Implement Code 128B in .NET Mobile Wireless Communications

Mobile Wireless Communications using none tobuild none for web,windows application Bar Code Types ow-balance none none equation (9.21). Compare this equation with that found assuming exponential-distributed cell dwell times.

(See problem 9.3 and eq. (9.

6).) (c) Explain why these two handoff probabilities are given by PN = Prob [Tn > TN ] and PH = Prob [Tn > TH ]. (d) Show, starting with (9.

4) and the de nitions of PN and PH in (c) above, that these two probabilities are, in general, given by (9.19) and (9.20), respectively.

9.7 Consider the case of the one-dimensional cell of Fig. 9.

4, with all mobiles moving at the same velocity Vc , equally likely in either direction. (a) Show that the new-call cell dwell-time density function, distribution function, and probability of handoff, are given, respectively, by (9.23), (9.

24), and (9.25). (b) Take the three examples considered in the text: a macrocell whose length L = 10 km with mobiles moving at 60 km/hr, a macrocell of length L = 1 km and the same mobile velocity, a microcell of length L = 100 km with 5km/hr mobile velocities.

Calls are all exponentially distributed, with a 200 second average value. Show the new-call handoff probabilities are given, respectively, by 0.316, 0.

86, and 0.84 (see Table 9.2).

Do these numbers agree with intuition Do they agree with the nding that the probability of new-call handoff in this case of constant mobile velocity depends on the dimensionless parameter L/Vc , 1/ the average call length (call holding time) Repeat the calculations for some other examples, with one or more of the three parameters changed. Consider a one-dimensional cell of length L, as in Fig. 9.

4. The mobiles move at velocities randomly chosen from a uniform distribution with maximum velocity Vm . Focus on the new-call dwell times and probability of new-call handoff.

(a) Fill in the details of the derivations in the text of the dwell-time density function, probability distribution, and handoff probability PN for this case, and show they are given, respectively, by (9.27), (9.28), and (9.

29). (b) Repeat the calculations of PN for the three cases of 9.7(b), with Vm = 2Vc in all cases.

The average call length is 200 seconds in all cases. Show the results obtained agree with those shown in Table 9.2: PN = 0.

30, 0.78, 0.76.

Show how these results agree with those expected from the dependence on the dimensionless parameter a L/Vm . Select some other examples and repeat the calculations, comparing the results obtained with those expected, based on variations in this parameter. This problem treats the one-dimensional cell example of problems 9.

7 and 9.8, but focuses on the determination of the dwell-time distribution and probability of handoff PH for calls handed off from another cell. (a) Show that, for mobiles all moving at the same velocity Vc , PH is given by (9.

30). (b) Show that, if mobiles move at speeds randomly chosen from a uniform distribution of maximum value Vm , the density function of the dwell-time distribution is given by (9.31), while the probability of handoff is given by (9.

32).. Performance analysis (c) Use the none none three examples of problem 9.7(b) to nd the probability of handoff in each case. The average call length is 200 seconds.

Show the results given in Table 9.2 are obtained. Choose some other examples, as in problems 9.

7(b) and 9.8(b), and show how the results obtained verify the dependence on the parameter a L/Vm in the random velocity case. 9.

10 Consider the three one-dimensional cell examples of problem 9.7(b). (These appear in the text as well.

) Find the ratio of handoff call arrival rate to new-call generation rate in each case. Neglect the blocking and handoff dropping probabilities in doing these calculations. Compare results with those provided in the text.

The text describes a procedure for determining the probability distribution of the channel holding time distribution in the case where the mobile dwell times within a cell are not exponentially distributed. This is described through the use of equations (9.33) (9.

37a). (a) Derive (9.37a) following the procedure outlined in the text.

Note that call lengths must be assumed to be exponentially distributed to obtain this result. (b) Focus on the one-dimensional cell model discussed in the text. The channel holding time is to be approximated by an exponential distribution with the same average value.

This leads to (9.39) as the equation for the approximating average value. Evaluate this expression for the three examples of problem 9.

7(b). Mobiles are all assumed to be moving at the same xed speed, the speeds indicated in problem 9.7(b).

Compare the approximating average channel holding times found with those found by assuming an exponentially distributed channel holding time directly. (c) Repeat the guard-channel calculations of problem 9.4(c), assuming onedimensional cells, and using the approximating average channel holding times found in (b) above.

Compare the results with those found in problem 9.4(c). (See the appropriate entries of Table 9.

1 as well.) This problem focuses on the two-dimensional cell geometries considered in Section 9.3.

(a) Consider the circular cell geometry of Fig. 9.9.

Filling in the details of the calculations outlined in the text, show that the probability density function of the new-call cell dwell time is given by (9.52) or (9.52a), while the distribution function is given by (9.

53). Note that the analysis assumes all mobiles travel at the same constant velocity Vc . (b) Using the geometry indicated in Fig.

9.10, show, following the analysis indicated in the text, that the probability density function of the handoff call dwelltime distribution is given by (9.56a), with the distribution function given by (9.

57). Mobiles are again assumed to be traveling at a constant velocity. (c) Calculate the probability of new-call handoff PN and the probability PH of a handoff call again handing off for the three examples of Table 9.

3 and compare with the results indicated there. (a) Use (9.61) to calculate the approximating average channel holding time for the three two-dimensional examples of Table 9.

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