Analysis

Via the mathematical equations and theoretical computation, the routing complexity and maintenance load are used to analyze the efficiency of compared schemes. We analyze the complexity of average cases rather than initial cases or worst cases, because the average performance is mapping to the results of repeating simulated experiments.

4.1. Routing complexity

One P2P scheme combined with one ad hoc routing protocol provides the P2P service on MANET. We use AODV as an example. AODV is a popular hop-by-hop routing protocol, and it always establishes the P2P communication on demand. P2P solution can search data via flooding or DHT query. The flooding query is suitable for dynamic topology, but the DHT query is efficient. We compare GPMS with other schemes including the flood-query and DHT-query over AODV.

In flood-query over AODV, a peer searches a source via flooding the query, whose complexity O(n) is well-known. Every query is forwarded on demand by intermediate node via AODV, whose complexity O(log n) is well-known. Therefore, the routing complexity of flooding over AODV is O(n log n).

In DHT-querying over AODV, a peer searches a source via DHT-based approach, whose complexity is well-known O(log n). The complexity of AODV is well-known O(log n).

Therefore, the routing complexity of DHT-querying over AODV is O((log n)²).

In GPMS, a peer searches a source via FPRT, which inherits DHT, thus its complexity is O(log n). The routing path is derived via FPRT to avoid the choice of on-demand intermediate node. The complexity of IPv6 routing via hop-by-hop routing header is O(1). Therefore, the routing complexity of proposed scheme is O(log n).

4.2. Maintenance load

Maintenance load means that each peer requires the maintenance load of P2P overlay when overlay is changed.

In flood-query over AODV, a peer usually discovers its members for reactive query, so the proactive overlay maintenance is unnecessary. Each peer just checks the arrival or departure of its member during the P2P communications, and the load is O(1) trivially. In addition, the maintenance load of AODV is well-known O(n) due to rediscovery. Therefore, the maintenance load of flooding over AODV is O(n).

In DHT-query over AODV, a peer maintains its DHT for indexing peers and files, and the maintenance load of DHT is well-known O(log n). AODV reestablishes a P2P communication without rediscovery due to the proactive maintenance of DHT, and the reestablishment of hop-by-hop path is well-known O(log n). Therefore, the maintenance load of DHT-querying over AODV is O((log n)²).

In GPMS, a peer maintains its FPRT for path information and service cache. Both updates of path information and service cache cost O(log n). Because FPRT shares the finger table and routing table, the maintenance of ad hoc routing is O(1). Therefore, the maintenance load of GPMS is O(log n). In summary, the routing complexity and maintenance load are summarized as Table 4.1 illustrated.

4.3. Routing overhead

Table 4.1: A summary of P2P over MANET schemes.

Routing complexity Maintenance load Flood-querying over AODV O(n log n) O(n)

DHT-querying over AODV O((log n)²) O((log n)²) The proposed cross-layer O(log n) O(log n)

In our proposed forwarding scheme, we can assume a probability that the i^th peer creates a multimedia packet in a given time t is p. The event b_i represents the process among n peers, and a sequence b1, b2, b3, … can be defined via Bernoulli formula:

P(b_i = 1) = P(i^th peer speaks) = p,∀ i and i ∈ n

P(bi = 0) = P(i^th peer calms) = 1 – p (3)

At some time t, the probability that k peers create multimedia packets simultaneously is P_K. PK(k) = Ckn

p^k (1 – p)^{n – k} (4)

Therefore, the probability that a peer creates h packets in m time slots is P_H is similar to Equation 4 theoretically.

P_H(h) = C_h^m p^h (1 – p)^{m – h} (5)

For one peer, tj can be defined that j^th packet is created in an inter-arrival time. Then the probability that a peer creates h packets in a given time t is P_T.

PT(t) = P(bi is true AND h – 1 packets are created in the first t – 1), for each i

= P(bi = 1) · PH(h – 1), while based on t – 1 for t ≥ h

= p · C_{h – 1}^{t – 1} p^{h – 1} (1 – p)^{t – h}

= Ch – 1t – 1

p^h (1 – p)^{t – h} (6)

And the expected time of h packets is E_H(h).

EH(h) = E(t1) + E(t2) + … + E(th), E is expected function

= 1/p + 1/p + … + 1/p = h/p (7)

The Bernoulli formal can be applied to an analog of Poisson process in a continuous time. We can define that the rate of packet created is λ in a given time t. The probability that k peers create packets in t is PN(k, t).

P_N(k, t) = e^–λt (λt)^k / k!, while λt = h = E_H(h) × p (8) Therefore, the expected value of duplicated packets is simplified as EN.

E_N(n) = Σ_k P_N(k, t) × k × n (9)

The fixed λ, t, n can derive the EN(n) for the low bound of packet duplications in the proposed hop-by-hop forwarding scheme.

4.4. Compared schemes

File sharing, voice communication, and video streaming are the live applications of P2P over MANET. According to the analysis of routing complexity, maintenance load, and routing overhead, we summarize the compared schemes as Table 4.2 illustrated, and list the descriptions.

 ORION (Optimized Routing Independent Overlay Network) [29] is based on an application layer overlay combined with the reactive ad hoc routing protocol for file sharing to guarantees high data rates and low transmission overhead over MANET.

ORION integrates Gnutella [6] query processing and overlay network construction with AODV routing discovery. Gnutella is a flooding base, so ORION belongs to the flood-querying over AODV.

 MADPastry (Mobile AD hoc Pastry) [15] is a file sharing application, and it belongs to the DHT-querying over AODV. MADPastry uses Pastry [9] proximity awareness to reduce the overhead without flooding. Pastry routing table indexes and hashes the mobile nodes.

 ACT (Audio Conferencing Testbed) [18] is based on OLSR to set up a meeting for group of people in WiFi MANET. ACT uses the minimum spanning tree to minimize the latency of audio dissemination to the whole network. Every peer must maintain its minimum spanning tree to deliver data by itself. ACT predicts the disconnection and mobility to

Table 4.2: The comparison of schemes.

File sharing Voice communication Video streaming

Flood-querying over AODV/ OLSR ORION ACT Smart Gnutella

DHT-querying over AODV/ OLSR MADPastry CLAPS MP2PS

shorten the service interruption time.

 CLAPS (Cross-Layer And P2P based Solution) [19] is based on the combination of tree-based overlay and OLSR extension. CLAPS assumes that the physical routing topology can be provided by OLSR, which sends cross-layer message to optimize overlay.

The source peer maintains a minimum spanning tree as its overlay. The minimum cost is computed via link distance packaged in cross-layer message, and the spanning tree is recomputed periodically to keep the overlay proximity.

 Smart Gnutella [20] enhances the original Gnutella to suit for MANET and for the real-time application. Because the periodic ping/ pong and broadcast can assist in routing maintenance, Smart Gnutella adopts AODV as the ad hoc routing protocol. Therefore, Smart Gnutella belongs to the flood-querying over AODV.

 MP2PS (Mesh-based P2P Streaming) [21] is a live streaming application, and it belongs to the DHT-querying over AODV. MP2PS provides real-time streaming with scalability and availability over MANET. MP2PS adopts mesh-based live streaming application, Joost [30], and no retransmission on wireless network, UDP, and on-demand ad hoc routing protocol, AODV.