An Internet Gateway Access-Point Selection Problem for Wireless Infrastructure Mesh Networks Shigeto Tajima, Teruo Higashino Graduate School of Information Science and Technology Osaka University {tajima, higashino}@ist.osaka-u.ac.jp
Nobuo Funabiki, Shoji Yoshida Department of Communication Network Engineering Okayama University
[email protected]
Abstract
can be easily and inexpensively deployed, compared with the wired network only.
This paper presents a study of the gateway access-point selection problem for the wireless infrastructure mesh network (WIMNET). WIMNET is a wireless mesh network composed of multiple access-points (APs) that communicate mutually using radio transmissions, and all the traffics to/from the Internet go through the limited number of gateway APs. Thus, the selection of these gateway APs often determines the whole performance of WIMNET, because heavy congestions at gateway APs and their peripheries can drastically increase the delay and the link failure due to radio interferences. In this paper, we define a cost function to minimize the total traffic in WIMNET in order to reduce congestions and present a simple algorithm. Through simulations using the newly developed WIMNET simulator, we show the effectiveness of our approach.
As a practical and stable wireless mesh network, we have studied the wireless infrastructure mesh network (WIMNET) that adopts only access points (APs) as wireless routers [3]. Each AP in WIMNET uses radio transmissions for both communications with associated hosts and adjacent APs. This function of wireless communications between APs is called the wireless distribution system (WDS). Since the same radio transmission channels are usually shared among APs and hosts in one WIMNET, simultaneous communications by adjacent APs and hosts may cause radio interferences and thus, intolerable degradations of the network performance. To avoid interferences as best as possible, the optimization of locations and radio channels of APs is essential in WIMNET. Therefore, we have proposed several algorithms for these purposes.
1. Introduction Recently, with the wide spread of the broadband Internet, using of a variety of information data bases and network services on the Internet have increased. Particularly, strong demands for the Internet access in every place including stations, airports, and other public places, have been raised, as wireless network interfaces by mobile personal computers (PCs) and personal digital assistances (PDAs) have become very small and low costs. As a result, wireless mesh networks [1, 2] have extensively been studied in academics and industries as the key technology to realize this Internet access mobility. A wireless mesh network is a multihop network composed of multiple wireless routers, where communications between routers are realized by radio transmissions, in addition to communications between hosts and routers. Thus, adopting the wireless mesh network, the local area network (LAN) covering a wide area
When WIMNET is used as a gateway LAN to the Internet, at least one AP must be performed as a gateway to it. Because every traffic to/from the Internet goes through one of these gateway APs, their selection can strongly affect the performance of WIMNET, even if locations and channels of APs have been optimized by algorithms [3]. Besides, gateway APs determine routing paths between APs and the Internet, which influence congestions of non-gateway APs. In this paper, we formulate this problem of the gateway AP selection in WIMNET, and present its simple algorithm, to design the highly efficient WIMNET topology. For this formulation, we newly define the cost function to minimize the total traffic between APs, in order to minimize the transmission delays and the link failures. We evaluate our approach through extensive simulations using the WIMNET simulator that has been also developed by our group to evaluate various optimization algorithms for WIMNET, including the AP allocation algorithm and the AP channel assignment algorithm [4]. Here, we briefly note some related works. [5] presents
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communication request appears only between an AP and one of gateway APs in WIMNET.
3. Gateway AP selection problem and algorithm Figure 1. WIMNET topology
an algorithm to place the minimum number of gateway APs in a wireless neighborhood network that satisfies required flows from houses under link capacities. [6] introduces the common gateway architecture for adhoc networks, where multiple APs are connected with one Internet gateway and an adhoc routing protocol is applied for routing to the gateway. [7] proposes a gateway discovery algorithm based on the dynamic adjustment of the scope of the gateway advertisement packet. The rest of this paper is organized as follows: Section 2 describes the outline of WIMNET in this paper. Section 3 presents the formulation of the gateway AP selection problem and our algorithm. Section 4 shows simulation results by the WIMNET simulator for evaluations. Section 6 provides the concluding remarks with future works.
2. Outline of WIMNET WIMNET in this paper assumes that at any AP, two wireless communication protocols assigned different frequency bands, namely IEEE802.11a and IEEE802.11b/g, can be used at the same time, and at any host, only one protocol of IEEE802.11b/g is available. There are plural radio transmission channels that are not interfered mutually in each protocol. Thus, we assume that IEEE802.11a is used for communications between adjacent APs, and IEEE802.11b/g is used for communications between hosts and their associated APs, so that their simultaneous transmissions do not cause interferences between these two communications. At any AP, the location, the signal output intensity, and the radio channel can be fixed manually or by using their algorithms [3]. Then, the topology of WIMNET can be described by a directed graph as shown in figure 1, where a circle and a square represents an AP and a host respectively, and an edge represents the radio transmission link between them. Note that Since each AP or host is usually assigned a different signal output intensity, some edges can be unidirectional in the topology graph. WIMNET can also assume that most communications are performed between hosts in WIMNET and servers in the Internet including the mail server and the web server. Therefore, in the following discussions, we suppose that a
3.1. Problem Formulation The gateway AP selection problem requests us to select a given number of APs as gateways to the Internet for a given WIMNET topology. As the objective function of the problem, we define the minimization of the total traffic that is transmitted between APs in this multihop network. This reduction of the total traffic can reduce the communication delay and the link failure by AP communications. Actually, we define the following cost function E as the total traffic for minimization: E=
n ∑
mhop(APk ) · hk
(1)
k=1
where n is the number of APs, mhop(APk ) represents the number of hops or links at the shortest route in terms of hop counts between the kth AP and its closest gateway AP, and hk represents the expected number of hosts associated with this AP. Here, we believe that hk can be roughly estimated by counting the number of seats in stations or stadiums that are typical application fields of WIMNET. mhop(APk ) can be calculated by applying the Dijkstra shortest path algorithm [8] . Now, we summarize the formulation of the gateway AP selection problem as follows: • Inputs: – a number of gateway APs (m) – WIMNET topology – expected numbers of associated hosts with APs (hk ) • Outputs: – a set of gateway APs • Objective condition: – minimization of cost function (E)
3.2. Algorithm Our algorithm for the gateway AP selection problem simply selects the required number of APs that minimize the cost function E in 1 among all the possible combinations. This number of possible combinations is actually bound by O(nm ), where n is the number of APs and m is the number of gateway APs, and both n and m are usually small ones.
Often, a limited space in the application field of WIMNET such as a seating space in stations, is more congested than other space in the field. To take advantage of this situation, we introduce a heuristic to improve the network performance and to reduce the computation time with a smaller search space by the algorithm. In this heuristic, at least one AP inside this congested space is always selected as a gateway AP. Here, we note that our final goal of the gateway AP selection problem is the maximization of the network performance, not the minimization of the defined cost function E. Because the network performance cannot be calculated at this gateway AP selection stage, the cost function E is introduced for the descriptive purpose as an alternative way of calculation.
4. Simulation Model for Evaluation 4.1. WIMNET Simulator To evaluate the performance of our gateway AP selection approach for WIMNET, the WIMNET simulator has been developed on a PC (Pentium4 3.0GHz) coded by C. This simulator describes the least behaviors of infrastructure wireless communications for evaluations of optimization algorithms including this gateway AP selection without details of communication protocols, so that a large scale simulation can be possible within reasonable CPU time. In the WIMNET simulator, every wireless link is activated synchronously using a single clock, where one time span is called a time slot and the duration time is set 10ms in our simulations. In one time slot, one packet can be transmitted through a wireless link if no interference occurs. If interference occurs between activated links, every packet transmission becomes void, and packets stay at their source hosts or APs. Then, the wait counter (WC) for the source (host or AP) of any interfered link is incremented by 1, and the waiting time is randomly assigned between 1 and (2W C − 1) where the source halts from the next link activation. Based on the M/M/1 queuing model, the communication request is generated at each host, where the request arrival follows the Poisson distribution, and the duration time (the packet size) follows the exponential distribution. As described before, we assume that every communication request is held between a host inside WIMNET and a server in the Internet, going through a gateway AP. Thus, in WIMNET, any request is described by a communication between a host and its closest gateway AP. Either the uplink or the downlink is randomly selected for each request. When a request arrives at a host, it transmits the generated packets to its associated AP that is the closest one from the host. If this AP is not a destination (gateway AP) of the request, it forwards the packets to its adjacent AP along the route to
the destination, as the multihop transmission. The communication route has been selected beforehand as the shortest path from the AP to the destination. As the summary, the inputs of the WIMNET simulator are locations, signal output intensities, and radio channels of the APs, the gateway APs, the routes between APs and gateway APs, the request arrival rate, and the average packet size. The outputs for the performance evaluation are communication delays and failure rates.
4.2. Host Migration Model To express movements of hosts for dynamic evaluations of WIMNET, we have proposed the seating space model (SSM) as a more practical host migration model than the popular random waypoint model (RWM) [9] in adhoc network researches. In SSM, a seating space suitable for mobile communications exists inside the network field, where more hosts stay than in other space. This seating space is surrounded by a wall with only one doorway. As in RWM, any host moves directly to a randomly selected next destination with a randomly selected constant speed, after it stays for a certain time called pause time. In SSM, a point inside the seating space is more frequently selected than those in other space, so that more hosts stay in the seating space. When the wall exists along the moving path from the current position to the destination, the host bypasses the wall. The radio transmission signal in the WIMNET simulator can be propagated without degradations to any place within the distance from the source that is given by the signal output intensity. However, if a wall exists before that place, this distance becomes half, to consider effects by propagation obstacles.
4.3. Simulation Parameters In our simulations using the WIMNET simulator, the network filed is given by 400 × 400meters, the seating space inside the field is by 100 × 100meters, the number of mobile hosts is 100, the number of gateway APs m is selected among 1, 2 and 3. The request arrival rate is given by 1/180s−1 , which means that each host tries to communicate with a server every three minutes on average. The average packet size is varied from 10 to 100, to investigate the change of the performance when the traffic load in WIMNET is changed. In order to avoid the bias of random numbers, a total of five instances with different random numbers for each case are generated, and their average results are used in evaluations. Figure 2 shows an example WIMNET topology with 32 APs. The small square inside the field represents the seating space with a doorway along the lower side. In this instance, the expected number of associated hosts to one AP in the
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Figure 2. An example of WIMNET topology with 32 APs.
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seating space is about 2.4 times of that to an AP in the other space.
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5. Simulation Results
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Figure 3. Delay (m = 1)
reduce it. Figures 7 and 8 show the distributions of average delays of successful communications and failure rates for m = 1 and m = 2 respectively, when the gateway APs are selected by our algorithm (white circles) and randomly (black circles). These figures indicate that the delay and failure rate can be widely different, and they are correlated to each other. Actually, our algorithm selects appropriate gateway APs with the small delay and failure rate.
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This section discusses the performance evaluation of our gateway AP selection approach using the WIMNET simulator. First, in order to verify the effect of our heuristic of preferentially selecting an AP inside the congested space such as the seating space in SSM, we evaluate a case with heuristic (A in graphs) and another case without heuristic (B). Actually, in the case with heuristic, when two or more gateway APs are selected, at least one AP in the seating space and at least one AP in the other space are always selected. For comparisons, the case of the cost function E without considering the expected number of associated hosts hk (C) is also simulated to verify the validity. Table 1 shows the average, the minimum, and the maximum route length or hop count for communications between an AP and its closest gateway AP that is selected by our algorithm. The average and maximum route lengths by A is usually longer than those by B or C, and the difference becomes small as the increase of m. This result indicates that our algorithm does not always select APs as gateways to minimize the number of hop counts for AP communications. Figures 3 and 4 show the delays of successful communications for m = 1 and m = 2 respectively. Figures 5 and 6 show the failure rates for both cases. The comparison between B and C indicates that the consideration of the expected number of AP associated hosts in our algorithm can drastically reduce both the delay and the failure rate. The comparison between A and B indicates that our heuristic can improve them slightly. Table 2 shows the CPU time of A and B when m is increased from 1 to 3. As the number of gateway APs increases, the CPU time difference also increases, which supports the advantage of our heuristic to
ave. 3.431 3.030 2.994 2.570 2.470 2.201 2.091 2.091 1.893
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Figure 5. Failure rate (m = 1) 35
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Figure 6. Failure rate (m = 2)
6. Conclusion This paper has presented our study of the Internet gateway access point selection problem for the wireless infrastructure mesh network (WIMNET). The effectiveness of our approach with the defined cost function and the heuristic is verified through simulations using the newly developed WIMNET simulator. The optimization of the number of gateway APs and evaluations using a real WIMNET will be in our future studies.
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Figure 8. Distribution of network performance by gateway AP (m = 2)
[3] Y. Nomura, N. Funabiki, and T. Nakanishi, “A proposal of access-point channel assignment algorithm and an evaluation of access-point allocation algorithm in wireless infrastructure mesh networks,” Proc. 3rd ANWS, pp.1-13–1-16, Jan. 2006. [4] S. Yoshida, N. Funabiki, and T. Nakanishi, “A development of wireless infrastructure mesh network simulator,” Proc. 3rd ANWS, pp.1-9–1-12, Jan. 2006.
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Table 2. CPU time (m = 3) |GW | 1 2 3 A 0.000026 0.000037 0.000434 B 0.000027 0.000083 0.002603
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