INVESTIGATION ON THROUGHPUT OF A MULTI HOP NETWORK WITH IDENTICAL STATION FOR RANDOM FAILURE

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1 International Journal of Computer cience and Communication Vol. 2, No. 2, July-December 2011, pp INVETIGATION ON THROUGHPUT OF A MULTI HOP NETWORK WITH IDENTICAL TATION FOR RANDOM FAILURE Manish hrivastava 1 and Ravi ahu 2 1,2 LNCT, Bhopal maneesh.shreevastava@yahoo.com, ravisahucs2@gmail.com ABTRACT In Multi-hop networks stations may pump more traffic into the networks that can be supported, resulting in high packet-loss rate, re-routing instability unfairness and random failures problems due to this effect system efficiency. In this paper formula s has been used for numerical simulation from [2], by using this formula s we obtain throughput of a multi hop network with identical station against random failure and perform numerical simulation and identify bottlenecks for a multi hop network composed of a series of workstations separated by buffers, the stations which is subject to random failures. The extended formula is used to compute throughput and analyzes the flow of jobs in the network. The simple analytical result that shows the mathematical relationship between the key system parameters, These include the ratio λ/µ that is used to determines a station s efficiency and the ratio Bµ/ that provides a measure of buffer effectiveness during failures of the multi hop network. The comparisons show when number of station increases the efficiency of the network rapidly drop against low frequent failure and slightly drop against high infrequent failure. The results also show that increasing the buffer size provides a much bigger improvement in throughput for short frequent failures than for long infrequent failures. Keywords: Wireless Networks, Ad Hoc Networks, Multi-hop Network, Random Failure, Low Frequent Failure, High in Frequent Failure. 1. INTRODUCTION An important measure of performance for a multi hop network is the system throughput. Various analytical models have been developed to analyze throughput and identify bottlenecks for a multi hop network composed of a series of workstations separated by buffers the stations which are subject to random failures. The throughput of a network depends on each station s speed (processing rate) and reliability, the sizes of the buffers and the number of stations. In this paper formula s has been used for numerical simulation from [2], by using this formula s we obtain a throughput and then perform simulation. The basic throughput formula given by Alden s model [1] this model considers two workstations and provides a building block for design a model for multi workstation. Alden s model is developed for the general case in which stations can have different speeds and reliabilities, and buffers can have different sizes. ince the model yields analytical equation for throughput performances, it can be used to compute throughput for two such workstation very efficiently and the use of this model to derive a throughput formula for multi hop network with identical station against random failure. The extended formula is used to compute throughput and analyzes the flow of jobs in the network. In this paper formula s has been used to compute throughput for a special case of a multi hop network with identical stations and buffers of equal sizes which is subject to random failure from the general equations of the model. The paper utilizes simplifications for the special case in which simple analytical result that shows the mathematical relationship between the key system parameters. These include the ratio λ/µ that determines a station s efficiency and the ratio Bµ/ that provides a measure of buffer effectiveness during failures of the multi hop network. 2. RELATED WORK Alden s model developed by [1] [2] it is a network consisting of two stations in series, separated by a buffer. Jobs flow to be processed at each station. The two stations are each subject to failures, which affect the throughput. Each station is characterized by its fixed speed (processing rate) and reliability parameters (failure rate and repair rate). depicts the two-station line. The buffer holds jobs processed at the first station and waiting to be processed at the second station. If the buffer is full, the first station is blocked and cannot release a job or process new jobs. If the buffer is empty, the second station is starved and has no new jobs to process. Alden s model captures the impact of blocking and starving on the number of jobs in the buffer, and uses results on the buffer content to obtain the line s throughput. The equations are developed in the model for a two-station line in general and for a line where the two stations have equal speeds. In his work, the parameters for the general

2 560 International Journal of Computer cience and Communication (IJCC) two-station model are first defined, and the assumptions are stated. The basic equations developed in the model for stations with equal speeds are then presented. These equations are used to derive a formula for throughput in the special case of identical stations (i.e., stations with equal speeds, and also equal failure rates and repair rates). In this section, J. J. Garcia-Luna-Aceves & Yu Wang [3] presents the work on throughput and fairness of collision avoidance protocols in ad hoc networks. In the first part of his work, he use a simple model to derive the saturation throughput of MAC protocols based on an RT-CT-data-ACK handshake in multi-hop networks. The results show that these protocols outperform CMA protocols, even when the overhead of RT/CT exchange is rather high, thus showing the importance of corrects collision avoidance in random access protocols. More importantly, it is shown that the overall performance of the sender initiated collision avoidance scheme degrades rather rapidly when the number of competing nodes allowed within region increases, in contrast to the case of fully-connected networks and networks with limited hidden terminals reported in the literature, where throughput remains almost the same for a large number of nodes. The significance of the analysis is that the scalability problem of contention-based collision-avoidance MAC protocols looms much earlier than people might expect. the performance gap is smaller as perfect collision avoidance protocols also begins to suffer from exceedingly long waiting time. In the second part of his work, he proposes a framework to address the fairness problem in ad hoc networks systematically. The framework includes four key components: Exchange of flow contention information, adaptive and stable back off algorithm, hybrid collision avoidance handshake, and special processing for two-way flows. He proposed some specific algorithms to realize the framework and the resulting scheme, called topology aware fair access (TAFA), was evaluated through computer simulations against the IEEE MAC protocol and a hybrid channel scheme proposed in his literature. In this section Ping Chung Ng [4] presents his work on to identify the maximum throughput that can be sustained in an multi-hop network. His contributions are three-folds: he has shown that uncontrolled, greedy sources can cause unacceptably high packet-loss rate and large throughput oscillations. Judicious offered load control at the sources, however, can eliminate these problems effectively without modification of the multi-access protocols. He has established an analytical framework for the study of the effects of hidden nodes and carrier-sensing operation. This analysis allows one to determine whether the system throughput is hidden-node limited or spatial-reuse limited. In particular, he has shown that the maximum sustainable throughput is limited by two factors: (i) the vulnerable periods which depend on the numbers of hidden nodes and the fraction of airtime in the time horizon when hidden-node collisions may occurs; (ii) the number of nodes within a carrier-sensing region and the total airtime used up by them. 3. PERFORMANCE PROBLEM IN MULTI HOP NETWORK In a multi-hop network, sources may inject more traffic into the network that can be supported. This may result following problems: 1) High packet loss rate due to selective packet dropping Attack, 2) Re-routing instability, 3) Random failure, 4) hort frequent failure, 5) High infrequent failure. 4. FORMULA FOR NUMERICAL IMULATION In this paper formula s has been used for numerical simulation from [2], by using this formula s we obtain throughput and perform numerical simulation, the purpose of this section is to extend the two-station Throughput formula into multi station throughput formula, so that it applies to a multi hop network with any number of stations. The extension holds under the same assumptions given by [1,2] as for the two-station model. We consider again the special case of identical stations, and assume also that the buffers between stations all have the same size. Figure 1 depicts the multi hop network of general length. The parameters for this case are: (i), the station speed (jobs per hour), (ii) λ, the failure rate (failures per hour), (iii) µ, the repair rate (repairs per hour), (iv) B, the buffer size (number of jobs), (v) M, (number of stations) To obtain a formula for throughput that includes the additional parameter M, we analysis the two station formula & extended to derive a throughput formula for multi hop network with identical station against random failure. Figure 1: Multi Hop Network of General Length with Identical tations and Buffers of Equal ize [2]

3 Investigation on Throughput of a Multi Hop Network with Identical tation for Random Failure 561 Functional form: ρ 2λ 1 + λ /(() µ + /)/ f1 M1() λ 1( µ /) + f2 M + Bµ µ (1) Where f 1 (M) and f 2 (M) are functions to be determined. The function f 1 (M) provides the M-station generalization for the impact of station failures, independent of the buffers in the line, while f 2 (M) accounts for the impact of buffers specifically. Consider first the standard result for an M-station with no buffers. The throughput in this case is given by [2]. ρ = (2) 1 + M λ / µ Putting B = 0 in (1) gives ρ = 1 + λ / µ + [() f M/ ] λ µ (3) Compare (1) & (2) with the Buzacott result, and then obtain the following form for the function f 1 (M) : f 1 (M) = M 1 and substitute it in (3) 1 ρ = 1 + λ / µ + [( M 1) λ / µ ] (4) The simplest form for f 2 (M) is a linear function, f 2 (M) = km, where k is a constant. Function, the Impact of buffers is proportional to M. For the special case of M = 2, With this comparing Alden s model equation and (1) gives f 2 (2) = 1/2. Thus, in terms of k, we have 2k = 1/2 or k = 1/4, and hence f 2 (M) is given by f 2 (M) = M/4 (5) Putting f 1 (M) and f 2 (M) in (1), then obtain the following approximate expression for throughput of an M-station network: ρ M 2λ 1 + λ / µ + [( M 1) λ / µ ]/ 1 + 1( + /) Bµ 4 µ (6) Note: In this paper formula s has been used for numerical simulation from [2], by using this formula s we obtain throughput and perform numerical simulation and the extension given by formula preserves the basic relationships between parameters, as seen in the Alden s model Formula s from [1]. These include the ratio / that determines a station s efficiency, and the ratio B / that provides a measure of buffer effectiveness during failures. 5. REULT & DICUION Table 1 tation Parameter Values used in Throughput Comparisons [2] MTBF(mean time MTTR (mean / between failures) time to repair) ( jobs/h) ( failures/h) (repairs/h) (min) (min) hort frequent failures Long infrequent failures This section compares the throughput using formula given by (6). The comparisons are made for the given values of the station parameters, λ, and µ, and a range of different No. of station M and buffer sizes B. Following figures show the efficiency of multi hop network, is to perform numerical simulation had done with different values and data against random failure, short frequent failures and long infrequent failures Figure 2: Throughput Comparison

4 562 International Journal of Computer cience and Communication (IJCC) respectively. The continuous curves show throughput of the multi hop network, the results indicate that the throughput of the network rapidly drops with the increase in the number of station for different buffer sizes B against random failure. The comparisons show when number of station increases the efficiency of the network rapidly drop against low frequent failure and slightly drop against high infrequent failure. These results show that increasing the buffer size provides much bigger improvement in throughput for short frequent failures than for long infrequent failures. Figure 2 depicts the performance results for the throughput of the network rapidly drops with the increasing number of station. Figure 2(b) depicts the size is 1, The comparisons show at instant when number of station is M=16 the efficiency of the network is almost 30% against low frequent failure at the same instant the efficiency of the network is almost 45% against high infrequent failure. Figure 3 depicts the performance results for the throughput of the network rapidly drops with the increasing number of station. Figure 3(b) depicts the size is 3, The comparisons show at instant when number of station is M=16 the efficiency of the network is almost 39 % against low frequent failure at the same instant the efficiency of the network is almost 54% against high infrequent failure. Figure 4 depicts the performance results for the throughput of the network slightly drops with the increasing number of station. Figure 4(b) depicts the size is 6, The comparisons show at instant when number of station is M=16 the efficiency of the network is almost 40% against low frequent failure at the same instant the efficiency of the network is almost 57% against high infrequent failure. Figure 3: Throughput Comparison Figure 4: Throughput Comparison

5 Investigation on Throughput of a Multi Hop Network with Identical tation for Random Failure 563 Figure 5: Throughput Comparison Figure 6: Throughput Comparison Figure 5 depicts the performance results indicate that the throughput of the network slightly drops with the increasing number of station. Figure 5(b) depicts the size is 12, the comparisons show at instant when number of station is M=16 the efficiency of the network slightly improve when size of buffer increases at present scenario the efficiency is almost 45% against low frequent failure at the same instant the efficiency of the network is almost more than 60% against high infrequent failure. These following figures show that increasing the buffer size has a much improvement in throughput for short frequent failures than for long infrequent failure. Figure 6 depicts the performance results for the throughput of the network rapidly increases with the increasing number of buffers. Figure 6(a) and 6(b) shows the performance of throughput for high infrequent failure is good as compare as low frequent failure when increasing the buffer size and fix the number of station is 20 for these present scenario, The comparisons show at instant when number of Buffer is B=16 the efficiency of the network is almost 45% against low frequent failure at the same instant the efficiency of the network is almost more than 60% against high infrequent failure. These following figures show that increasing the buffer size has gives a bigger improvement in throughput for short frequent failures than for long infrequent failures. 6. CONCLUION In multi-hop networks, stations may pump more traffic into the networks that can be supported, resulting in high packet-loss rate, re-routing instability unfairness and random failures problems due to this effect system efficiency. In this paper formula s has been used for numerical simulation from [2], by using this formula s we obtain throughput and perform numerical simulation and identify bottlenecks for a multi hop network composed of a series of workstations separated by buffers and the stations which is subject to random failures. Following above Figures depicts the performance results for the efficiency of the network against low frequent failure and high infrequent failures, the results indicate that the throughput of the network slightly drops with the increase in number of station. Above figures shows the performance of throughput for high infrequent failures is good as compare as low frequent failures when increasing buffer size. The comparisons show when number of station increases the efficiency of the network rapidly drop against low frequent failure and slightly drop against high infrequent failure. These results also show that increasing the buffer size provides much bigger improvement in throughput for short frequent failures than for long infrequent failures.

6 564 International Journal of Computer cience and Communication (IJCC) REFERENCE [1] J. M. Alden, Estimating Performance of Two Workstations in eries with Downtime and Unequal peeds, Research Publication R&D-9434, General Motors R&D Center, Warren, Michigan, [2] Dennis E. Blumenfeld And Jingshan Li, An Analytical Formula for Throughput of a Production Line with Identical tations and Random Failures, [3] J. J. Garcia-Luna-Aceves And Yu Wang, Throughput and Fairness of Collision Avoidance Protocols in Ad hoc Network. [4] Ping Chung Ng, Throughput Analysis of IEEE Multi-hop Ad hoc Networks, Paper Identification Number: TNET [5] J. A. Buzacott, Prediction of the Efficiency of Production ystems Without Internal torage, International Journal of Production ystems, Vol. No. 3, [6] J. A. Buzacott and J. G. hanthikumar, tochastic Models of Manufacturing ystems, Prentice-Hall, New Jersey, [7] N. Bhalaji and Dr. A. hanmugam, Reliable Routing against elective Packet Drop Attack in DR based MANET, Journal of oftware, 4, No. 6, August [8] Bounpadith Kannhavong and Abbas Jamalipour, A- OLR: ecurity Aware Optimized Link tate Routing for MANET, IEEE Communications ociety Publication in the ICC [9] Akansha aini and Harsh Kumar, Effect of Black Hole Attack on AODV Routing Protocol in MANET, IJCT, 1, Issue 2, December [10] N. Bhalaji, Dr. A. hanmugam, Defense trategy using Trust based Model to Mitigate Active Attacks in DR Based MANET, Journal of Advances in Information Technology, 2, No. 2, May [11] Jiejun Kong, Xiaoyan Hong, An Identity-Free and On- Demand Routing cheme against Anonymity Threats in MANET, IEEE Transaction on Mobile Computing, 6, August 2007.