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Congestion Control in Wireless Sensor Network Using Innovative Modification to the Increase Decrease Algorithm Sanu Thomas and Thomaskutty Mathew

Abstract A new method of congestion control in wireless sensor network is described. We make a simple but innovative modification to the increase–decrease algorithm to improve its performance. The modification proposed uses additive as well as multiplicative operation for both increase and decrease phases. Basically, we consider a single-link multisource system. The sending rate of each source is optimally controlled to prevent the congestion of the common link. The rate control at sources is adjusted based on the feedback signal from the destination. The proposed method provides efficiency, fairness, and fast convergence.

Keywords Congestion control Additive multiplicative increase Additive multiplicative decrease Fast convergence Shortest path trajectory

1 Introduction In a modern clustered Wireless Communication Network (WSN) [1], the major data flow is from the sensors toward the Base Station (BS) or sink through the Cluster Heads (CHs). In general, the geographically disbursed sensor nodes acquire data from their surroundings and send them to the BS. This is basically a many-to-one type communication. Therefore, the occurrence of congestion is higher here compared to one-to-one or one-to-many type of communication systems. When the WSNs are deployed for event-driven applications, the sudden spurt in the communication traffic, triggered by the detection of events, may cause severe congestion and result in data loss [2]. Therefore, proper congestion control measures are S. Thomas (&) School of Technology and Applied Sciences, Mahatma Gandhi University, Regional Center, Pullarikunnu, Kottayam, Kerala, India e-mail: [email protected] T. Mathew School of Technology and Applied Sciences, Mahatma Gandhi University, Regional Center, Edappally, Kochi, Kerala, India © Springer Nature Singapore Pte Ltd. 2018 H. Vasudevan et al. (eds.), Proceedings of International Conference on Wireless Communication, Lecture Notes on Data Engineering and Communications Technologies 19, https://doi.org/10.1007/978-981-10-8339-6_1

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S. Thomas and T. Mathew

very much needed in such scenarios. Another major cause for congestion is the lower available bandwidths prevalent in wireless networks. In this paper, we consider the case of event-driven WSN where the traffic density is high. For WSNs, we have several congestion control protocols [3, 4] like PSFQ, CODA, ESRT, and so on. We use a modified version of additive increase and multiplicative decrease method which is popular in TCP congestion control. Additive Increase Multiplicative Decrease (AIMD) is the standard algorithm used in TCP for congestion control. AIMD can be easily adapted for wireless communication also [5–8]. Our paper is mainly inspired by the work of Chiu and Jain [9]. In AIMD, the increase is purely additive but the decrease is purely multiplicative. In the existing AIMD, the convergence is slower and oscillatory. In our proposed algorithm, we use additive and multiplicative increase as well as additive and multiplicative decrease. We control the relevant flow rate in a multisource closed-loop system to avoid the congestion at the receiver. This is mainly due to the limited bandwidth of the shared channel that carries the data from the multiple sources to a single receiver. In our control system, we achieve faster convergence using the shortest path approach without oscillations to reach the convergence point. Instead of binary feedback as in [9], we use full feedback.

2 Network Model and Assumptions Consider a cluster-based Wireless Sensor Network (WSN) having N nodes. We assume a single Cluster Head (CH) which collects data from the sensor nodes and then forwards it to the Base Station (BS). The basic model is shown in Fig. 1. The CH collects data from N sources which are the respective sensor nodes. The data sources are named as S1, S2, …, SN. The corresponding flow rates from these sources are represented by x1 ðtÞ; x2 ðtÞ; . . .; xN ðtÞ in packets per second. Here, xi ðtÞ is the transmission rate in the present time slot t, from source Si for i = 1 to N. The present rate vector xðtÞ is written as xðtÞ ¼ ½x1 ðtÞ; . . .; xN ðtÞ

ð1Þ

The capacity of the forward link from the CH to the BS is taken as C packets per second. C mainly depends on the bandwidth and quality of the forward link. It also depends on the receiver buffer size and the processing delay at the BS. For the specified session, we assume that C is constant. Congestion in the link is avoided when the total incoming rate is less than or equal to C. Therefore, at a time slot t, this condition is represented as N X i¼1

xi ðtÞ C

ð2Þ

Congestion Control in Wireless Sensor Network … Fig. 1 Cluster head with N sources

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Base Station (BS) Feedback Link

Forward Link (Capacity = C ) ∑ xi (t) Cluster Head (CH)

xN(t)

x2(t)

x1(t) S2

S1

C

SN

The CH receives the value of C at regular intervals from the BS through the feedback link and the CH in turn controls xi(t)’s such that constraint (2) is satisfied.

2.1

Basic Working of the Rate Control

We propose a linear closed-loop negative feedback control system to control the rates. The control system block diagram for x1 ðtÞ is shown in Fig. 2. In Fig. 2, the reference input is b1 which is the final desired output, multiplicative factor is a1, error term is e1(t), and the present controlled output is x1 ðtÞ. For the sake of clarity, we introduce a two-source rate control system which can be extended for multisource. Let the two sources be S1 and S2 with the respective flow rates x1 ðtÞ and x2 ðtÞ: Now with N = 2, constraint (2) becomes

e1(t) = b1 –x1(t)

Fig. 2 Control system block diagram for the single source rate control

b1

x1(t+1) Unit Delay

a1 x1 (t)

Governing Eq. :

x1 (t)

x1 (t)

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x1 ðtÞ þ x2 ðtÞ C

ð3Þ

The sum ðx1 ðtÞ þ x2 ðtÞÞ is called the utilization [10]. Therefore, the maximum possible utilization is C. At steady state both x1 ðtÞ and x2 ðtÞ remain stable. They do not vary with respect to time. Therefore, the desirable steady-state value corresponding to the cumulative maximum C is b1 þ b2 ¼ C

ð4Þ

Here, b1 and b2 are the desired steady-state (equilibrium) values of x1 ðtÞ and x2 ðtÞ; respectively. Fairness between x1(t) and x2(t). Assuming equal priority, between S1 and S2, the condition for fairness at equilibrium requires, b1 ¼ b2 and then, b1 ¼ b2 ¼ C=2:

2.2

Control Equations

The discretized control equations for x1(t) and x2(t) can be expressed as x1 ðt þ 1Þ x1 ðtÞ ¼ a1 ðb1 x1 ðtÞÞ

ð5Þ

x2 ðt þ 1Þ x2 ðtÞ ¼ a2 ðb2 x2 ðtÞÞ

ð6Þ

The flow rates x1 ðtÞ and x2 ðtÞ are governed by (5) and (6), respectively. Additive–Multiplicative Increase and Additive–Multiplicative Decrease. The RHS of (5) has a1 b1 ; an additive term and a1 x1 ðtÞ; a multiplicative term. Therefore, the increase/decrease in x1 ðtÞ is both additive and multiplicative. (The same property holds true for x2 ðtÞ.) Therefore, our method is called the Additive–Multiplicative Increase and Additive–Multiplicative Decrease (AMIAMD) algorithm. Equilibrium at b1 : From Eq. (5), we see that whenever x1 ðtÞ [ b1 ; the RHS of (5) is negative. Therefore, x1 ðt þ 1Þ x1 ðtÞ is also negative. This means x1 ðtÞ decreases as t increases. That is, x1 ðtÞ moves toward b1 : On the other hand, if x1 ðtÞ\b1 ; the RHS of (5) is positive. Hence, x1 ðtÞ increases toward b1 . Thus, whenever x1 ðtÞ is away from its equilibrium value b1 ; it moves toward b1 : Finally, when x1 ðtÞ ¼ b1 ; the RHS of (5) is zero and x1 ðtÞ neither increases nor decreases. Thus, b1 is the equilibrium or the steady-state value of x1 ðtÞ:

2.3

Pictorial Representation

From (5) and (6), x1 ðtÞ and x2 ðtÞ are calculated iteratively for t = 0, 1, 2,…, and so on. To see the control action pictorially, we represent the variations in x1 ðtÞ and

Congestion Control in Wireless Sensor Network …

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Fig. 3 State space diagram for x1 and x2

x2 ðtÞ as a trajectory of vector xðtÞ; where xðtÞ ¼ ðx1 ðtÞ; x2 ðtÞÞ; in a two-dimensional space (state space) as shown in Fig. 3. In Fig. 3, the capacity parameter C is taken as 1. The capacity line (also called efficiency line [9]) is drawn from (0, 1) to (1, 0). On this line, x1 ðtÞ þ x2 ðtÞ ¼ C. The region above this line represents the overloaded (congested) link and the region below this line represents the underloaded (uncongested) link. The trajectory of xðtÞ is shown in the region where x1 ðtÞ þ x2 ðtÞ C: This is the region below the capacity line. In Fig. 3, xð0Þ ¼ ðx1 ð0Þ; x2 ð0ÞÞ ¼ ð0; 0:3Þ; is the starting point (initial values of xðtÞ) for t = 0). The equilibrium point (final value) is b ¼ ðb1 ; b2 Þ ¼ ð0:5; 0:5Þ. The trajectory gb, for our AMIAMD, is shown in green. The other trajectory gd, in cyan, is for AIMD which is shown for the purpose of comparison. The LHS of (5) gives Dx1 ðtÞ and the LHS of (6) gives Dx2 ðtÞ which are also shown in Fig. 3.

3 AMIAMD Multisource Rate Control Algorithm Here, we have N sources. The rate vector xðtÞ is given by (1) subjected to the constraint (2). Then, the discretized multisource rate control is given by (5) which is generalized and rewritten as

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xi ðt þ 1Þ ¼ xi ðtÞ þ ai ðbi xi ðtÞÞ

ð7Þ

for i = 1 to N and for t = 0, 1, 2,… etc. For equal priority sources, bi is calculated for all i’s as, bi = (C/N). In (7), ai’s are equal and taken as, a1 ¼ a2 ¼ ¼ aN ¼ a with 0 < a < 1. The value of a is chosen by the designer. Then, (7) is further rewritten as xi ðt þ 1Þ ¼ xi ðtÞ þ aðbi xi ðtÞÞ ¼ abi þ xi ðtÞð1 aÞ

ð8Þ

The rate control is governed by (8) for i = 1 to N. The error ei ðtÞ is defined as ei ðtÞ ¼ bi xi ðtÞ

ð9Þ

When ei ðtÞ reaches a value less than certain threshold, emin ; we assume that the system has reached the steady state. emin is selected by the designer. In general, emin is in the range 0.1–0.5% of bi. Hence, at steady state, ei ðtÞ\emin for i = 1 to N.

AMIAMD is a continuous process. It works continuously as long as the communication process between the CH and the BS is active. If there are no changes in C or N, it continues in the steady state. The controller receives the feedback value C


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from the BS, periodically (or asynchronously in an emergency). The control system at CH knows N. If C or N changes, then at step 4, algorithm AMIAMD calculates the new bi and the control process continues accordingly.

3.1

Comparison Between AMIAMD and AIMD

We compare our AMIAMD with the standard increase–decrease rate control algorithm AIMD [9]. The criteria used for the comparison are transient response, fairness, network utilization, convergence, and distributedness. Transient Response. The variation of x1 ðtÞ for AMIAMD and AIMD with respect to time is shown in Fig. 4. For AMIAMD plot, a1 = 0.24, x1 ð0Þ ¼ 0:3; x2 ð0Þ ¼ 0 and b1 = 0.5. For AIMD plot, the additive parameter = 0.06 and the multiplicative factor = 0.08. Initial and final values of AIMD are same as in AMIAMD. Fairness. When sources have equal priority, fairness means the equality among xi ðtÞ’s for all i’s and t’s. In AMIAMD, fairness is achieved during the steady state but not during the transient state. In AIMD, fairness is maintained with respect to increments during the increase phase. The differential behavior between AMIAMD and AIMD is shown in Fig. 5. In AIMD described by Chiu and Jain [9], for the two-source scenario, the transition is along the line fxð0Þ d g which is purely additive and then along {d − b} where the trajectory is oscillatory. The path fxð0Þ d g is a 45°-degree line from x(0) to d that represents equal increments in x1 ðtÞ and x2 ðtÞ: This happens in AIMD because, when underloaded (congestion-free zone), the increase is purely additive. Therefore, the transient path in AIMD is fxð0Þ d g. Along this path, the horizontal and vertical increments are equal ðDx2 ðtÞ ¼ Dx1 ðtÞÞ. Thus, in AIMD, fairness is maintained for increment phase only but not for actual values x1 ðtÞ and

Fig. 4 Transient response of x1(t) in AMIAMD and AIMD

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Fig. 5 Transient responses of AMIAMD and AIMD in state space

x2 ðtÞ. After the increase phase, the path crosses point d and then reaches b along {d − b} with oscillations as shown in Fig. 5. In AMIAMD, during the transient phase, it is not possible to maintain actual or incremental fairness, because AMIAMD follows the shortest path fxð0Þ bg to reach b as fast as possible. Network utilization. It is the sum of all xi ðtÞ’s at the steady state [10]. In AMIAMD, when xi ðtÞ’s reach their goal, ei ðtÞ’s \emin and the channel utilization is maximum and is very near to C. In AIMD, also the utilization reaches the maximum value C. Convergence. AMIAMD achieves fast convergence, because it follows the shortest path fxð0Þ bg. In AIMD, the path traversed is fxð0Þ d g and then {d − b}. During the {d − b} phase traversal, AIMD produces oscillations as shown in Fig. 5. This two-segment traversal increases the convergence time of AIMD, whereas the single straight shortest path fxð0Þ bg traversed by AMIAMD scheme naturally converges faster. This is the strongest advantage of AMIAMD. Distributedness. AMIAMD is a centralized algorithm, unlike AIMD. In AMIAMD, the control system is implemented in the CH to whom the sensor nodes report. The CH receives full feedback instead of binary feedback (as in AIMD) [9]. Therefore, all the information, regarding the number of active sources and initial/ starting rates is known to the CH. Therefore, the centralized control operation is not difficult or expensive. If required, AMIAMD can be altered into a distributed algorithm.


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4 Conclusions An innovative modification is made to the popular AIMD algorithm. The modification incorporates both additive and multiplicative increase as well as additive and multiplicative decrease. Basically, it is a centralized algorithm which uses negative feedback to achieve optimal data rate allocations while avoiding congestion. It can be modified into a distributed one. The strength of the algorithm is fast convergence and non-oscillatory transient response. It provides affirmative corrective action among different sources while incrementing (or decrementing) the rates originating from unequally placed starting points. The proposed algorithm can be modified to implement weighted and max-min fairness rate control.

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