Capacity region and minimum energy function for a variety of delay-tolerant mobile unicast ad hoc networks are studied by using a cell-partitioned model. First, theorems about analytical expressions of network capacity and upper bound of minimum energy function are proposed and proved. Algorithm aiming at maximizing capacity and minimizing energy cost is presented and analyzed by Lyapunov drift method. Second, these two theorems are applied to several types of ad hoc networks. Expressions of network capacity and minimum energy function are obtained. Third, capacity property of a type of hybrid ad hoc networks is analyzed in detail. Relationship among limitation of capacity, node density, and coverage of base stations are investigated. Numerical analysis and simulation are carried out.In this subsection, we illustrate in detail the cell-partitioned model used in this paper, which is of the same kind as the ones used in, for example, [7,8]. Cell-partitioned model is a simple model for ad hoc networks but can serve as a useful theoretical model for analyzing more complex networks. Some assumptions seem very simple, but this model indeed provides meaningful bound on performance of ad hoc networks [7]. More thorough discussions about assumptions used in this model can be found in [7,8]. We consider networks without using mix or multicast packets, such as network coding or cooperative communication, which may increase the network capacity and reduce energy costs.
Network model.In cell-partitioned model, network is divided to C nonoverlapping cells (not necessarily of the same size/shape) ( Figure 1). Time is slotted, that is, time is divided to timeslots.There are a finite number of virtual communication channels that can be used in each cell. Here, "virtual communication channels"(hereinafter shorted for "channels") mean different types of communication resource. (For example, for the network in [7], in each cell, at most, one node is allowed to transmit, so there is only one channel in each cell. For the network in [8], in each cell, to a node in the same cell, at most, one node is allowed to transmit at a rate R 1 ; meanwhile, to a node in adjacent cells, at most, one node is allowed to transmit at a rate R 2 , so there are two channels in each cell. And for the network analyzed in Section 4, which is a simple model of hybrid ad hoc networks, in each cell, by using the pure ad hoc networks resource, at most, one node is allowed to transmit; meanwhile, by using the base stations resource, at most,
Traffic model.There are N unicast sessions in the network, with each node being the source of one session and the destination of another session. Packets are assumed to arrive at the source of each session i according to an i.i.d. arrival process A i .t/ with mean rate i . At a timeslot, nodes receive Wirel. Commun. Mob. Comput. 2016; 16:825-849