[Part one begins a discussion of the basic evolution of wireless networks and how position location could be considered from the networking point of view. Part two offers a general overview of wireless mobile ad hoc networks and sensor networks, including their evolution, applications, and issues such as connectivity and scalability.]
5.2 MOBILITY IN WIRELESS NETWORKS
Mobility is a very important issue that needs to be addressed in a wireless network, since it limits capacity. For example, in a cellular network with no mobility, we can establish a capacity criterion based on the Erlang-B formula. Channels will be occupied by users that contribute to traffic so that a cell with C channels will have a blocking probability given by the formula.
If we allow users to move, then some users from adjacent cells will hand off their calls to the cell of interest, producing a higher occupancy state in the cell and thus a higher blocking probability. This simple reasoning shows how mobility could limit capacity.
In the following sections, we introduce some aspects of mobility that need to be considered to balance the capacity–coverage trade-off that mobility causes.
5.2.1 Capacity and Coverage Issues
Demand for wireless services has increased, which in turn brings new issues to consider such as mobility management for service providers . One of the major objectives of a telecommunications system is to offer a service of excellent quality based on user requirements. In order to evaluate how a network or a communication system performs, we need to define measures that quantify the effects of varying parameters such as demand and capacity. In wireless networks, we allow users to move from area to area, thereby causing handoffs in the network. A user requesting service for the first time from the network is considered a new call.
Two of the most important performance measures in wireless networks are the new call and the handoff blocking probabilities [34, 48]. The handoffs are a fundamental feature in cellular systems;their performance and efficiency strongly depend on the use of adequate algorithms. For cellular communication systems, to ensure mobility and capacity, to maintain the desired coverage areas, and to avoid problems of interference, it is necessary to correctly assign the calls to the corresponding service areas in the entire cell and in the entire network.
In a CDMA network, soft handoff has been modeled considering overlapping areas, such as in Kwon and Suang , Miranda-Guardiola and Vargas-Rosales , and Scaglione et al. . Admission of handoffs is done using one of three criteria. The first is to consider handoffs and new call arrivals equally for occupancy of the channels, the second reserves channels to give priority to handoffs, and the third sends them to a queue if no channel is available. Several performance evaluation algorithms have been introduced for these handoff strategies (e.g., see  and ) for reservation and queueing strategies and in McMillan  for the reservation and no-reservation strategies.
In a simplistic way, we can see each i-th cell as a resource with Ci channels offered Poisson traffic for new calls with λi calls per time unit, with exponential channel residence times with mean 1/µi . This would translate to considering each cell as an M/M/Ci/Ci system with performance provided by the Erlang-B formula,
But we need to see that each cell receives offered traffic due to handoffs from adjacent cells, as shown in Figure 5.12. And since the success of the new call traffic depends directly on the available capacity of the cell to which it is being offered, and the handoff calls depend on the available capacity of the cell from which it comes, we can see a cellular network such as that in Figure 5.12 as a Jackson-type network of queues  as shown in Figure 5.13.
FIGURE 5.12 Traffic offered to cell in wireless network.
FIGURE 5.13 Cellular network as Jackson network of queues.
In Vargas-Rosales et al. , it was shown that this viewpoint has a solution for the blocking probability of new calls and handoff calls with channel reservation. The fundamental idea in this model is that the traffic offered to a cell is given by the new call traffic plus handoffs that have already been accepted in an adjacent cell; that is, if we denote as vij the handoff traffic offered from cell i to cell j, Bi as the new call blocking in cell i, and Bhi as the handoff blocking in cell i, we can obtain the handoff rate out of cell j offered to cell i as
where Aj is the set of neighboring cells to cell j, and pij is the routing probability from cell i to cell j. The first term in Equation (5.2) is due to those new calls offered to cell j that are accepted and after a residence time, handed off to cell i with probability pji. The second term is due to all handoff calls that are offered and accepted into cell j from its adjacent cells and then handoff to cell i.
One can see that this model helps us to comprehend the effects that mobility has on performance by varying the routing probabilities to increase the proportion of handoff calls being offered. To solve for the blocking probabilities, one needs to consider a fixed point because Equation (5.1) is in terms of traffic offered, and this depends on new call arrivals plus handoffs as given by Equation (5.2). Equation (5.1) now also has traffic from both arrivals of new calls and handoff calls. This immediately tells us that traffic increases, and thus blocking also increases; that is, capacity in terms of number of possible simultaneous users active is reduced.
This model has been evaluated for FDMA and TDMA in Vargas-Rosales et al. , and for CDMA in Miranda-Guardiola and Vargas-Rosales . In addition, the use of reservation degrades performance for the type of traffic with higher bandwidth requests. Even though these networks have limitations in terms of interference levels, it has been shown that relevant limitations are due to blocking .
It is well known that CDMA capacity depends on the processing gain and the bit energy-to-noise ratio, but from another viewpoint, we can consider a scenario where a central cell is influenced by interference from an infinite number of rings (tiers), each of which contains cells transmitting at the same frequency with users working with perfect power control. The scenario was considered with homogeneous circular cells of radius R in Munoz et al. . The advantages of using such a model are that we get bounds on the interference levels even for an infinite number of cells due to the infinite number of rings surrounding the center cell.
In the model, the same number of users for each cell is considered, and in order to obtain the major influence of the users, in each cell all users are located at the closest point toward the center. The model used a simple propagation model with a path-loss exponent between 2. 5 and 4, and cell radius was varied to consider cases with a radius of 3, 5, and 10 km. In the worst-case scenario, a cell capacity of 20 users was obtained when the number of interferents was infinity. Voice activity and sectoring were considered as well. The important aspect of this result is that regardless of the number of interferents, the capacity of CDMA cells with perfect power control will be lower-bounded by 20. We must be cautious when referring to this number since in these conditions FDMA and TDMA would be useless due to interference. The final result of the analysis in  is provided by the following lower bound:
where N is the number of users in each cell, γ is the path-loss exponent, R is the cell radius, C/I is the carrier-to-interference level usually set to -15 db, and is the Riemann-Hurwitz function that converges for x > 1 and y > 0.
In general, network capacity also depends on limitations encountered by the underlying channels. These limitations determine the data rates at which one can transmit with small bit error rates (BERs). Once the physical layer provides a reliable link to transmit, then the network functions take place, consuming some of the available bandwidth in order to achieve network control. So in order to consider capacity in wireless networks, we have to see that channel capacity or single-user system capacity and multiuser capacity need to be integrated.
For networks with infrastructure, it is well known that the uplink will have a degraded performance once the number of users increases since interference will be an issue. The base station transmits at a certain power level in the downlink that is also affected by the amount of interference, creating a coverage problem in some areas since the downlink signal will not be received with as much power as it seems. We also know that higher frequencies will require higher sensibility from the receivers since received power is inversely proportional to frequency. For treatments of these capacity issues in single-user and multiuser systems, see Goldsmith .
For networks that have no infrastructure (i.e., reconfigurable networks such as ad hoc and sensor networks) capacity has been an important research issue. For these networks, it is not as simple since the concept of simultaneous number of users does not apply directly due to the distributed use of the bandwidth. In addition, issues such as bit rates, interference suppression, multiple access, geographic position, topology, connectivity, and reachability, among others, play an important role in determining the number of nodes that could be active at a given time in a network. Also, certain types of algorithms implemented could be improved if used in a distributed or cooperative way. Capacity in these networks has been studied in general , as has how mobility increases capacity when cooperation is used (e.g., see ).
The work of Grossglauser and Tse  contains a study of a network with no mobility with nodes generated randomly on a disk or sphere, and as the node density increases, the throughput per origin destination pair decreases with a bound determined by 1/sqrt(n). It was also shown that this is the best performance that one can get even with optimal cooperation in relaying, routing, and scheduling. One issue would then be scalability, since the result in Gupta and Kumar  gives practically a zero throughput when the network grows. In contrast, mobility can help maintain constant origin–destination pair throughput even when the network grows, as shown in Grossglauser and Tse . The result is based on the use of relaying as a form of multiuser diversity.