The equilibrium buffer fill distribution can be described by a set of differential equations assuming sources alternate asynchronously between exponentially distributed periods in ``on'' and ``off'' states. Figure 1 shows such a source. Note that the ``on'' to ``off'' probability is normalized to one and that the transitions represented are intensities.
Figure 1: Constant Bit Rate ``on''-``off'' ATM Source.
In addition, the probabilities that mobile sources have links to a given buffer are included. The sources represent mobile user nodes which are transmitting and receiving ATM traffic, and the buffer represents a switch as shown in Figure 2. The details of such a mobile ATM system implementation are described in the Rapidly Deployable Radio Networks (RDRN) Network Architecture  and .
Figure 2: Mobile ATM Sources before Handoff.
Figure 3 illustrates the handoff of a remote node from one switch to another. Note that the ``on''-``off'' CBR Source model is similar to the ``connected''-``disconnected'' status of the remote nodes as they handoff from one base station to another. This observation is used in developing the analysis for mobile ATM systems.
Figure 3: Mobile ATM Sources after Handoff.
In a fixed network, the queue fill distribution is determined for multiple constant rate on-off sources. However, it assumes that the number of sources remains constant over a sufficient period of time for the equilibrium probabilities to be valid. There are at least two ways of extending the analysis to a mobile cellular environment.
Consider the ATM cell queue fill distribution at the base station. The simplest, but least accurate extension is to determine the average number of channels used per cell area as . However, there is nothing to stop mobile units from concentrating in a small number of cell areas at some time. There is a hard limit on the number of sources a base station will accept because each base station has a limited number of ports. Once this number is reached, further handoffs into such a cell will cause their connections to terminate. Thus, determining how many codes to assign to a base station is a critical design choice, .
Note that code assignment can be dynamic, but this will not be considered here in order to help simplify the analysis. Also, cell areas can be designed to overlap . Although this can increase the probability of interference, it has a beneficial effect on handoff. When a mobile unit determines that a handoff is likely to occur and the cell it will enter has no channels available, the mobile unit can continue to use the cell within which it currently resides, and queue the handoff to the next cell. If a channel becomes available in the destination cell before the mobile leaves its current cell, the handoff can take place successfully. It would be interesting to see the effect of queuing the handoffs. Again, in order to keep the computation simple for this paper, this will not be considered.
This paper makes the simplifying assumption that each mobile unit is a single ATM source multiplexed at the base station. In general, each mobile unit would be a set of sources; however, this could again be a future extension of this paper.