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Mobile CBR Source Analysis

Assume that the number of mobile hosts in a cell area is independent of whether its CBR source is on or off. We can now modify the probability that i sources are on and the queue fill is less than x by incorporating the probability that there are at least i sources, shown in Equation 8.

  equation251

tex2html_wrap_inline858 is the probability that at time t, i sources are on, and the number of items in the buffer does not exceed x. tex2html_wrap_inline866 is the probability that there are at least i sources sending data to the buffer. tex2html_wrap_inline866 can be found from Equation 6 as follows,

equation261

The buffer fill distribution as defined in [1] is

  eqnarray266

Now that the channel equilibrium probabilities have been determined, we can account for the fact that the sources are mobile. Since the channel equilibrium probabilities have no dependence on time, the method of solution in [1] can be used with minor modifications,

  eqnarray270

From [1], tex2html_wrap_inline872 is the equilibrium probability that i sources are on, and the buffer content does not exceed x. Thus tex2html_wrap_inline878 is the probability that i out of N sources are simultaneously on. In the mobile environment, this is now,

equation274

The mobile extension from Equation 8 carries through [1] for example, equation (13) in [1] is now,

equation279

and

equation281

tex2html_wrap_inline884 is the right eigenvector of

equation284

where D and M are matrices used to represent the differential equation in Equation 10.

tex2html_wrap_inline886 is the generating function of . These values are useful in [1] for solving the equilibrium buffer fill differential equation. The remainder of the solution is straight forward from [1]. Thus it has been shown how an analysis of constant bit rate on-off sources which model fixed length ATM packet sources, is extended to a mobile environment.

Note that the analysis uses a technique which is more accurate than M/D/1 for the fixed size ATM cells, yet uses a memoryless analysis for the channel holding time distribution. This is a reasonable approach since the variable length channel hold times can be accurately modeled by a memoryless analysis, while the M/D/1 analysis yields optimistic results which can be replaced by the more accurate method in [1] as this section has described.

 


next up previous
Next: Example Up: Mobile Systems Analysis Previous: Mobile Node Analysis

Steve Bush
Sun Aug 25 17:38:45 CDT 1996