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    • Swathi .M, Dr.D.Kavitha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.204-209 Analyzing Delay Performance of Multi-hop Wireless Networks Swathi .M1, Dr.D.Kavitha2 1 Department of CSE, G.Pullareddy Engineering College, Kurnool, Andhra Pradesh, India Professor 2 Department of CSE, G.Pullareddy Engineering College, Kurnool, Andhra Pradesh, IndiaABSTRACT In this paper a multi-hop wireless destination. Or, data can be transmitted at highnetwork is considered to analyze the delay power, which means the data can be sent further andperformance. We assume that there is a fixed more quickly but the powerful transmission mayroute between a given source and destination interfere with transmissions from many other nodes.pair. The multi-hop nature of network may cause Multi-hop wireless is motivated by the fact thatcomplex correlations of the service process. In many embedded wireless devices are power-limitedorder to handle them, we propose a queue and cannot communicate directly with a distant basegrouping technique. An interference model is station or access point.assumed which is set based. With the help ofinterference constraints the lower bound of delay 2. DELAY ANALYSIS IN MULTI-HOPperformance is obtained. To achieve this WIRELESS NETWORKsystematic methodology is used. The simple-path Network delay is an important design anddelay-optimal policy we designed is used for performance characteristic of a computer network orwireless networks. Empirical studies revealed telecommunications network. The delay of athat our approach is good to optimize scheduling network specifies how long it takes for a bit of datapolicies and analyzing delay in multi-hop wireless to travel across the network from one node ornetworks. endpoint to another. It is typically measured in multiples or fractions of seconds. Delay may differIndex Terms slightly, depending on the location of the specificMulti-hop wireless network, delay, flow control, pair of communicating nodes. There is a certainwireless mesh network, optimization, queuing minimum level of delay that will be experienced dueanalysis, scheduling to the time it takes to transmit a packet serially through a link. Onto this is added a more variable1. INTRODUCTION level of delay due to network congestion. IP Wireless networks are growing at a network delays can range from just a fewtremendous rate and are fast becoming ubiquitous milliseconds to several hundred milliseconds. For abecause of the low cost, ease of deployment, large class of applications such as video or voiceflexibility, accessibility, and support for mobility. over IP, embedded network control and for systemThe market has been flooded with wireless enabled design; metrics like delay are of prime importance.devices such as mobile phones, laptops, PDA, The delay performance of wireless networks,sensors and so forth. It is natural to network these however, has largely been an open problem.devices to support exchange of information and The general research on the delay analysis wasservices. Such networks may be built on top of a progressed in the following main directions:fixed infrastructure or could be set up completely onan ad-hoc basis. It is important to understand the • Heavy traffic regime using fluid models:fundamental limits of these networks and design Fluid models have typically been used tocontrol policies that achieve the desired level of either establish the stability of the system or to studyperformance. the workload process in the heavy traffic régime. Multi-hop wireless networks utilize The maximum-pressure policy (similar to the back-multiple wireless nodes to provide coverage to a pressure policy) minimizes the workload process forlarge area by forwarding and receiving data a stochastic processing network in the heavy trafficwirelessly between the nodes. Multi-hop wireless regime when processor splitting is allowed.networks can provide data access for large andunconventional spaces, but they have long faced • Stochastic Bounds using Lyapunov drifts:significant limits on the amount of data they can This method is developed and is used totransmit. Data can be transmitted at low power over derive upper bounds on the average queue length forshort distances, which limits the degree of these systems. However, these results are orderinterference with other nodes. But this approach results and provide only a limited characterization ofmeans that the data may have to be transmitted the delay of the system. For example, the maximalthrough many nodes before reaching its final matching policies achieve O(1) delay for networks 204 | P a g e
    • Swathi .M, Dr.D.Kavitha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.204-209with single-hop traffic when the input load is in the each link is one packet in a slot. Delay performancereduced capacity region. This analysis however, has of any scheduling policy is influenced bynot been extended to the multi-hop traffic case, interference. In [5] the use of exclusive set of linksbecause of the lack of an analogous Lyapunov is used to demonstrate the single hop traffic. In thisfunction for the back-pressure policy. paper we define bottleneck as a set of links such that no more than one of them can simultaneously• Large Deviations: transmit. In [5] sharper upper bounds could be used. Large deviation results for cellular and However, in this paper our focus is to derivemulti-hop systems with single hop traffic have been fundamental bound on performance of any policy.to estimate the decay rate of the queue-overflow As per our consideration the lower bound analysis isprobability. Similar analysis is much more difficult an important step. In this regard [16] is similar tofor the multi-hop wireless network considered here, this paper. We also reengineer a back – pressuredue to the complex interactions between the arrival, scheduling policy whose delay performance is closeservice, and backlog process. to the lower bound. Our contributions in this paper Throughput and utility of a multi-hop are a new queue grouping technique; new techniquewireless network are important aspects of much of to reduce the analysis of queuing upstream of athe research conducted on such networks. In such bottleneck; derivation of a fundamental lower boundsystems and its applications like embedded network on the system wide average queuing delay of packetcontrol, system design, voice and video over IP in multi-hop wireless network; extensive discussionperformance metrics like delay plays a crucial role and numeral studies.and the delay is the open problem in such systems.As there are complex interactions over wireless 3. PROPOSED SYSTEM MODELnetworks, this problem is so complex and needs lot This section describes system model. Weof research. Furthermore, the interference in the consider a wireless network which is represented aswireless networks makes it worst. In this paper, we G = (V, L) where set of nodes in the network isuse a systematic methodology for delay analysis and represented by V and L denotes the set of links. Unitalso a scheduling policy in order to achieve delay capacity is associated with each link. We consider Nperformance with respect to lower bound. number of flows. Each flow contains source andWe analyze a multi-hop wireless network with many destination pairs (si, di). We assume a fixed routesource and destination pairs provided traffic and between source and destination nodes. Exogenousrouting information. The packet flow is as described arrival stream of each flow is computed as.here. A source node sends packets into network. Inturn the packets move through network and finallyreach the destination. Fig. 1 shows three flows The service time of a packet is considered apertaining to wireless multi-hop network. single unit. Another assumption is that the exogenous arrival stream of each flow is independent. Set of links where mutual interference is not caused and thus can be scheduled simultaneously are known as activations. Two hop interference model is used in the simulation studies as it can model the behavior of large class of MAC protocols. It is because it supports virtual carrier sensing which makes use of CTS/RTS message. FINDING AVERAGE DELAY LOWER BOUNDS For a given multi-hop wireless network, the methodology used to derive lower bounds on the system wide average packet delay. The network flows are partitioned into many groups and each group passes through a bottleneck. In the process the queuing of each is individually analyzed. TheFig. 1 Multi-hop wireless network with flows and intention behind grouping is to maximize the delaybottlenecks system wide. When a flow is passing a bottleneck, the sum of queues is lower bound both upstream and As the transmission medium is shared, at downstream. By using statistics of the exogenouseach node a packet is queued in its path and waits arrival processes, the computation of lower boundfor an opportunity for it to be transmitted. on the system-wide average delay is performed. TheScheduling can be done on two links that do not reduction of a bottleneck to a single – queue systemcause interference with each other. Such links are is justified by our analysis. A greedy algorithm hasknown as activation vectors. The unit capacity of 205 | P a g e
    • Swathi .M, Dr.D.Kavitha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.204-209been implemented that takes a system with flows context of wireless networks, the back-pressureand bottlenecks as input and generate a lower bound policy has been widely used to solve problems ofon the system-wide average packet delay. multi-hop wireless networks [4], [11]. The research community has realized the significance of studyingGreedy Partitioning Algorithm such policy in terms of delay, network stability and This algorithm is meant for dividing the complexity of interactions for different flows. Thewhole wireless network into many single – queue proposed policy is meant for managing queuessystems and get bound on expected delay. pertaining to flows in the decreasing order of size. This is considered from the source node to destination node. By using a value known as differential backlog this has been achieved. The differential backlog is used as the weight for the link and scheduling. The scheduling that is matching highest weight is considered. This is the reason this policy is referred to as back-pressure policy. This policy has been studied and applied to various networks of multi-hop nature such as tandem, clique and so on. Back-Pressure Policy The policy known as back-pressure canTABLE 1: shows greedy partitioning algorithm lead to large delays. This is because from the destination the backlogs are gradually larger. The A dynamic program can be used for flow of packets is from larger queue to a shorteroptimal partition. However, this approach is queue. Moreover the it is possible that some of thecomputationally expensive. For this reason in this links may remain idle. The result of this is that therepaper the greedy algorithm presented in table1 was will be larger delays at bottlenecks. Experimentsdeveloped in order to find average delay of a with this policy were done with various networkwireless network which contains bottlenecks. topologies such as tandem queue, dumbbell, tree and cycle. As per the results it likely that upstream4. DESIGN OF DELAY-EFFICIENT queues of a bottleneck grow long resulting in larger POLICIES delays. Observation for clique and tandem network Delay efficient scheduler designing is an is that increase in priority of packets close toimportant question in multi-hop wireless networks. destination results in reduction of the delay. TheDelay efficient policies can improve performance of same thing is known as LBFS rule in wiredmulti-hop wireless networks. It is extremely networks [12]. This policy is similar to the policy incomplex to derive delay optimal policies for general [16].purpose although it is easy for specific networkssuch as tandem and clique. The delay efficient 5. ILLUSTRATIVE EXAMPLEscheduler that works for all networks must satisfy The methodology we proposed and testedthe criteria given below. on various topologies mentioned in the previous It has to ensure high throughput. This is section is described here. We analyze the back- important for any scheduling policy to maintain pressure policy and the lower bounds. The lower delay under control. If not the delay may bounds can also help to understand back-pressure become infinite when loading is heavy. policy well. Maximal policy [1], [18] and back When there are multiple flows running in the pressure policies are compared. For a given network, these flows must be allocated interference model, we computed set of graphs resources equally. Therefore no flow is starved exclusively. We also implemented greedy algorithm. from sufficient resources. The non interference The arrival stream at each source is a collection of links are to be managed in such a way that no active and idle periods. The lower bounds are links are starved from resources and service as obtained using algorithm 1. For expected single starvation leads to an increase in the average queue system we use analysis proposed in [3]. delay of the system. As the network is dynamic and hascomplex interactions, it is not easy to achieve thecriteria or properties mentioned above. This is dueto lack of prior knowledge about flows and complexinteractions in a multi-hop wireless network. Aslearned from the work of [9], and [11], we opted touse back-pressure policy with fixed routing. In the 206 | P a g e
    • Swathi .M, Dr.D.Kavitha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.204-209Fig. 2 Simulation results for Tandem Queue Fig. 5 shows simulation results for tree topologyFig. 3 Shows simulation results for clique Fig. 6 Shows simulation results for cycle topology Fig. 7 Simulation results for linear networkFig. 4 shows simulation results for dumbbelltopology 207 | P a g e
    • Swathi .M, Dr.D.Kavitha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 6, November- December 2012, pp.204-2096. DISCUSSION AND RELATED WORK 7. CONCLUSION Research that has been done so far on In wireless networks delay analysis is anwireless networks [1], [4], and [11] focused on open problem which is very challenging. Thisstability of the system. The schemes developed for problem is further intensified with the interferencestability the back – pressure policy has been used. It in wireless network. For this reason, newis also known as throughput-optimal policy. approaches are essential to overcome this problemExpected delay analysis of these systems is focused in multi-hop wireless network. We focused on lowerin this paper. bound analysis in order to reduce the bottlenecks in In order to test the stability of increase it or multi-hop wireless systems. For specific wirelessstudy workload, fluid models are used. It is network we could a sample-path delay-optimaldescribed in [2] that maximum pressure policy can scheduling policy could be obtained. The analysisreduce workload process for heavy traffic networks. we did is general and works for a large class ofIn [4], [10], [13], and [14] stochastic bounds using arrival processes. It also supports channel variations.Lyapunoy drifts method is used to derive upper Identifying bottlenecks in the system is the mainbounds. This has not been extended to multi-hop problem and the lower bound helps in finding near-traffic. In order to calculate large deviation results optimal policies.for cellular systems large deviation results are usedin [17] and [20]. This kind of analysis for multi-hop REFERENCESwireless network is not easy as there are complex [1] P. Chaporkar, K. Kar, and S. Sarkar,interactions. 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