Source delay, the time a packet experiences in its source node, serves as a fundamental quantity for delay performance analysis in networks. However, the source delay performance in highly dynamic mobile ad hoc networks (MANETs) is still largely unknown by now. This paper studies the source delay in MANETs based on a general packet dispatching scheme with dispatch limit @math (PD- @math for short), where a same packet will be dispatched out up to @math times by its source node such that packet dispatching process can be flexibly controlled through a proper setting of @math . We first apply the Quasi-Birth-and-Death (QBD) theory to develop a theoretical framework to capture the complex packet dispatching process in PD- @math MANETs. With the help of the theoretical framework, we then derive the cumulative distribution function as well as mean and variance of the source delay in such networks. Finally, extensive simulation and theoretical results are provided to validate our source delay analysis and illustrate how source delay in MANETs are related to network parameters.
Overall delay (also called end-to-end delay), defined as the time it takes a packet to reach its destination after it is generated at its source, has also been extensively studied in the literature. For MANETs with two-hop relay routing, closed-form upper bounds on expected overall delay were derived in @cite_33 @cite_5 . For MANETs with two-hop relay routing and its variants, approximation results on expected overall delay were presented in @cite_11 @cite_20 . For MANETs with multi-hop relay routing, upper bounds on the cumulative distribution function of overall delay were reported in @cite_15 @cite_19 , and approximations on the expected overall delay were derived in @cite_24 . Rather than studying upper bounds and approximations on overall delay, some recent works explored the exact overall delay and showed that it is possible to derive the exact results on overall delay for MANETs under some special two-hop relay routings @cite_33 @cite_13 .
@cite_33 @cite_24 @cite_19 @cite_5 @cite_15 @cite_13 @cite_20 @cite_11
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Understanding the delay performance in mobile ad hoc networks (MANETs) is of fundamental importance for supporting Quality of Service (QoS) guaranteed applications in such networks. Despite lot of research efforts in last several decades, the important end-to-end delay modeling in MANETs remains a challenging issue. This is partially due to the highly dynamical behaviors of MANETs but also due to the lack of an efficient theoretical framework to depict the complicated network state transitions under such dynamics. This paper demonstrates the potential application of the Quasi-Birth-and-Death process (QBD) theory in MANETs delay analysis by applying it to the end-to-end delay modeling in broadcast-based two-hop relay MANETs. We first demonstrate that the QBD theory actually enables a novel and powerful theoretical framework to be developed to efficiently capture the complicated network state transitions in the concerned MANETs. We then show that with the help of the theoretical framework, we are able to analytically model the exact expected end-to-end delay and also the exact per node throughput capacity in such MANETs. Extensive simulations are further provided to validate the efficiency of our QBD theory-based models. Due to their simplicity and efficiency, the two-hop relay algorithm and its variants serve as a class of attractive routing schemes for mobile ad hoc networks (MANETs). With the available two-hop relay schemes, a node, whenever getting an opportunity for transmission, randomly probes only once a neighbor node for the possible transmission. It is notable that such single probing strategy, although simple, may result in a significant waste of the precious transmission opportunities in highly dynamic MANETs. To alleviate such limitation for a more efficient utilization of limited wireless bandwidth, this paper proposes a more general probing-based two-hop relay algorithm with limited packet redundancy. In such an algorithm with probing round limit τ and packet redundancy limit f, each transmitter is allowed to conduct up to τ rounds of probing for identifying a possible receiver and each packet can be delivered to at most f distinct relays. A general theoretical framework is further developed to help us understand that under different setting of τ and f, how we can benefit from multiple probings in terms of the per node throughput capacity and the expected end-to-end packet delay. We consider a network where each route comprises a backlogged source, a number of relays and a destination at a finite distance. The locations of the sources and the relays are realizations of independent Poisson point processes. Given that the nodes observe a TDMA ALOHA MAC protocol, our objective is to determine the number of relays and their placement such that the mean end-to-end delay in a typical route of the network is minimized.We first study an idealistic network model where all routes have the same number of hops, the same distance per hop and their own dedicated relays. Combining tools from queueing theory and stochastic geometry, we provide a precise characterization of the mean end-to-end delay. We find that the delay is minimized if the first hop is much longer than the remaining hops and that the optimal number of hops scales sublinearly with the source-destination distance. Simulating the original network scenario reveals that the analytical results are accurate, provided that the density of the relay process is sufficiently large. We conclude that, given the considered MAC protocol, our analysis provides a delay-minimizing routing strategy for random, multihop networks involving a small number of hops. We evaluate the end-to-end delay of a multihop transmission scheme that includes a source, a number of relays, and a destination, in the presence of interferers located according to a Poisson point process. The medium access control (MAC) protocol considered is a combination of TDMA and ALOHA, according to which nodes located a certain number of hops apart are allowed to transmit with a certain probability. Based on an independent transmissions assumption, which decouples the queue evolutions, our analysis provides explicit expressions for the mean end-to-end delay and throughput, as well as scaling laws when the interferer density grows to infinity. If the source always has packets to transmit, we find that full spatial reuse, i.e., ALOHA, is asymptotically delay-optimal, but requires more hops than a TDMA-ALOHA protocol. The results of our analysis have applications in delay-minimizing joint MAC routing algorithms for networks with randomly located nodes.We simulate a network where sources and relays form a Poisson point process, and each source assembles a route to its destination by selecting the relays closest to the optimal locations. We assess both theoretically and via simulation the sensitivity of the end-to-end delay with respect to imperfect relay placements and route crossings.