As mentioned earlier, different types of data traffic such as background, voice, and video are expected to be transmitted over VANETs. In order to support the transmission of different data traffic flows, the routes established between the communicating vehicles should meet the QoS requirements of each data type. The QoS requirements are defined by a set of service requirements known as QoS constraints that should be met by the network while transmitting a stream of data packets from the source to the destination [76]. QoS constraints can be grouped into additive and min-max concave constraints. Multiplicative constraints, e.g., packet loss rate, are included in additive class, because they can be transformed into additive constraints by using logarithms [77]. For additive QoS constraints, the value, sometimes called the weight, of the constraint along the route is the sum of the weights on the links forming that route. End-to-End delay and hop-counts are examples of additive QoS constraints. For min-max QoS constraints, the value of the constraint is the minimum or maximum weight on the links that form the entire route. Link bandwidth is an example of a min-max QoS constraint.
In a multi-hop vehicular network, identifying feasible routes subject to multiple QoS constraints features a Multi-Constrained (Optimal) Path (MC(O)P)
selection, which is proven to be an NP-hard problem [6] if the constraints are mutually independent [78].
Definition 1: Multi-Constrained Path (MCP) problem. Let G(V, E) be an undirected graph representing a vehicular communication network where V is the set of vehicles and E is the set of links connecting the vehicles. Let m denotes the number of QoS constraints Li where i = 1, 2, … m. Each link between two vehicles l(C1, C2) ∈ E is
associated with m weights corresponding to QoS constraints such that wi(C1, C2) ≥
0. The MCP problem is to determine if there is a route P from the source sr to the
destination de such that all the QoS constraints are met as described in the following
equation:
w
i(P)£L
i, i=1, 2, ... m
(2.10)Definition 2: Multi-Constrained Optimal Path (MCOP) problem. If there is more than one route that satisfies the condition in (2.10), then the MCOP problem is to return the one with the minimum weight with respect to a specific QoS constraint, e.g., the smallest hop-count.
2.3.2.1 Current QoS Routing Algorithms
Generally, there are two distinct approaches adopted to solve MC(O)P problems, exact QoS routing algorithms and heuristic and approximation routing algorithms. The main reasons to consider exact multi-constrained routing algorithms are as follows [79]. First, NP-complete behaviour seems to occur in specially constructed graphs, and some exact algorithms are equally complex as heuristics in algorithmic structure and running time on topologies that do not induce NP-complete behaviour. Second, by restricting the number k of paths explored during the path computation, the computational complexity can be decreased at the expense of possibly losing exactness. On the other side, heuristic and approximation algorithms try to reach an approximate solution to the optimal one in polynomial time. There is a wide range of available approximation algorithms to solve the MC(O)P problem. Swarm intelligence based and genetic routing algorithm approaches are relatively novel in this field.
In the literature, the appropriate algorithm proposed to solve the MC(O)P problem is usually determined by the number, type, and correlation of the QoS constraints of the problem. Routing with two QoS constraints is not an NP-hard problem unless both constraints are additive. For instance, when the constraints are bandwidth and delay, the MC(O)P problem is defined as a Bandwidth Restricted Path (BRP) problem [80]. Metric ordering is one of the main heuristics utilised to solve the BRP problem. Best paths are computed according to the highest priority metric and are then computed according to the second highest priority metric and so on. Widest-Shortest Path (WSP) and Shortest-Widest Path (SWP) are proposed algorithms to solve the BRP problem using metric ordering. In the WSP algorithm, the first metric to be considered is the number of hops. Shortest paths between the source and the destination are computed. If there is a tie, the path with the highest available bandwidth is chosen. In contrast, the SWP algorithm starts by finding paths with the highest available bandwidth then the shortest path among them is selected.
When the two QoS constraints are delay and cost, i.e., additive constraints, the MC(O)P problem is defined as a Restricted Shortest Path (RSP) problem. The proposed algorithms for solving the RSP problem start by computing the feasible paths according to the first constraint. From those feasible paths, they choose the optimal path according to the second constraint if such a path exists. Many heuristics have been proposed to solve the RSP problem, e.g., [78, 81, 82].
Finally, Metric Combination (MC) [83, 84], is another approach proposed to solve the MC(O)P problem when the QoS constraints are correlated. MC is used to reduce the complexity of the MC(O)P problem from multiple constraints to a single constraint. A conventional shortest path algorithm can then be used to find the feasible paths. The problem with this approach is that the combination rule for multiple QoS constraints is not direct and in most cases it is complicated.
2.3.2.2 Challenges of Multi-Constrained QoS Routing in VANETs
Due to the highly dynamic nature of VANETs and frequently changing topology, resource reservations are not applicable to provide QoS guarantees. Moreover, the proposed exact QoS routing algorithms are not suitable for solving the MC(O)P problem in VANETs for many reasons. In the exact QoS routing algorithms,
different strategies are followed to solve the MC(O)P problem, e.g., nonlinear definition of the path length [85], look-ahead feature [86], non-dominated paths [87], Dijkstra-like path search [83], and k shortest path [88]. Unfortunately, these strategies are not suitable for applications in VANETs. For instance, nonlinear definition of the path length is a fundamental block in achieving an exact solution to an MC(O)P problem. Equation (2.11) shows the nonlinear definition of path P that is known as Holder’s q-vector norm [89]
q m i q i i q L P w P l 1 1 ) ( ) (
(2.11)where lq(P) is the path length, wi(P) is the weight value of P according to the
constraint i where i = 1, 2, … m, and Li is the constraint value. In this way, the multi-
constrained problem is transformed to a single constraint problem enabling the use of Dijkstra’s shortest path algorithm [90] to solve it. It can be seen that the nonlinear definition in (2.11) does not allow prioritising one of the defined constraints over the others, an essential feature needed in VANETs, e.g., video data requires a highly reliable route but is tolerant to delays. Besides that, applying Dijkstra’s algorithm using the above nonlinear definition of the path length in multiple dimensions does not guarantee the subsections of the shortest paths are shortest paths [79]. Therefore, the k-shortest path strategy should be applied along with Dijkstra’s algorithm, which adds extra complexity to the routing process.
Furthermore, the look-ahead strategy is another fundamental block in conventional multi-constrained QoS solutions. It proposes to compute the shortest path tree rooted at the destination to each node in the network for each of the m link weights separately [79]. This proposal means that Dijkstra’s algorithm should be executed m times. Thus, the computational complexity becomes m times Dijkstra’s algorithm complexity plus m times the nonlinear length computation complexity. This is also not suitable for VANETs because it adds extra time complexity to the routing algorithm that is supposed to establish routes for real time applications.
On the other hand, distributed heuristic solutions such as swarm intelligence based algorithms display several features that make them particularly suitable for
solving MC(O)P problems in VANETs. They are fully distributed, so there is no single point of failure, the operations to be performed at each node are simple, they are self-organising, thus robust and fault tolerant, and they intrinsically adapt to traffic changes without requiring complex mechanisms [91]. Ant Colony Optimisation (ACO) is one of the most successful swarm intelligence techniques. It has been recognised as an effective technique for producing results for MC(O)P problems that are very close to those of the best performing algorithms [92]. In ACO, a number of artificial ants build solutions to an optimisation problem and exchange information on the quality of their solutions via a communication scheme that is reminiscent of the one adopted by real ants [22]. However, how and in particular to the degree which the ACO technique can improve multi-constrained QoS routing in VANETs is still unresolved.