Prediction Efficiency in Predictive p-csma/cd

Transcription

1 Prediction Efficiency in Predictive -CSMA/CD Mare Miśowicz AGH University of Science and Technology, Deartment of Electronics al. Miciewicza 30, Kraów, Poland Abstract. Predictive -ersistent CSMA rotocol is an imortant MAC solution develoed for networed sensor/control alications and used in Local Oerating Networs (LonWors) technology. The rotocol uses a built-in networ load rediction to suort collision avoidance. The aer resents an analytical study of rediction efficiency for a channel with collision detection. The aroach based on Marov chains is alied. The rocedure of erformance analysis includes the definition of transition robabilities of Marov chain for a secified load scenario, calculation of stationary distribution of contention window, and the robabilities of successful/unsuccessful transmission. It is shown that the redictive -CSMA rotocol manages to control the size of a cometition window in order to guarantee the sustained robability of a successful transmission. The simulative validation of analytical results is rovided. Keywords: MAC rotocols, sensor networs, erformance analysis, Marov chains. 1 Introduction Predictive -ersistent CSMA rotocol is the heart of LonTal/EIA rotocol used for communication between smart devices in Local Oerating Networs (LON, LonWors). LON has become a classic solution in building automation, and home networing, but is also used in a wide range of alications including, among others, semiconductor manufacturing, etrochemical industry, and wastewater treatment. In the redictive -CSMA the collision avoidance is alied for resolving uncoordinated access to the networ. In order to coe with overload situations, the redictive -ersistent CSMA has been designed as an adative version of ure -CSMA. In -ersistent CSMA, a node transmits with a fixed robability if the channel is idle, and defers the transmission with the robability (1-), when the channel is busy [10]. In the redictive -CSMA, the robability is variable and dynamically adjusted to exected traffic load using bacoff scheme. The advantage of the redictive -CSMA erformance is the throughut otimization, which consists in eeing a high throughut even if a networ is overloaded. Consequently, although the redictive -CSMA is a random access scheme, LonWors networs offer guaranteed bandwidth regardless of the offered traffic rate [3]. Under light traffic load, the redictive CSMA is reduced to the ure ersistent CSMA regardless of the structure of the traffic in a channel [3]. However, the destiny of rotocol oeration is to coe with high traffic corresonding to the

2 maximum load of a networ. This is when a user derives benefits from load rediction built in the rotocol. Indeed, transient overload situations occur in LonWors networed systems since the LON architecture is event-triggered and data are transmitted in resonse to external events [11,12]. The send-on-delta concet rather than the uniform samling is a natural sensor reorting aradigm in event-triggered alications [5,11]. Thus, the traffic in the channel is non-uniform and might be bursty. Moreover, the event-triggered architecture is rone to event showers, i.e. burst of correlated events, often released by a single hysical event that causes congestion of the system [9]. Such an effect occurs, e.g. when a fire is detected in a building by a number of redundant temerature and smoe sensors which begin to reort the event. The resent study addresses the issue of the asymtotic characteristics of redictive CSMA and the efficiency of rotocol redictability. Both roblems have not been quantitatively dislayed in the scientific literature. To recognize ability of the rotocol to coe with congestion, the channel must be stimulated by heavy load. We choose the saturation conditions for the rotocol analysis where each node has always a acet to send. The saturation condition reresents the largest ossible load offered to the networ by a given number of nodes, and constitutes the worst-case channel load. It is intuitively comrehensible that due to the negative feedbac, the size of the contention window grows with the number of cometing nodes. However, there is still no answer to the questions what is the relationshi between the mean size of cometition window and the number of nodes trying to access the channel. Several aers deal with the erformance analysis of redictive -ersistent CSMA rotocol [1-4, 6-8]. Main benefits of the redictive -CSMA scheme have been dislayed in [2]. Simulation analyses have been carried out in [3,7]. Analytical aroaches are resented in [6,8]. The former is the first comlex analysis of the redictive -CSMA based on the queuing theory. The latter follows a classical aroach develoed for the -CSMA in 70s [10]. The saturation throughut analysis for the redictive -CSMA without collision detection is resented in [4]. The resent study deals with the redictive -CSMA with collision detection, i.e. the redictive -CSMA/CD. With the collision detection the rotocol behavior is quite different from the one when a detection is absent since the contention window increase due to collisions is activated. Load scenario, where the acnowledged service (ACK) is used and all the transactions are unicast, is assumed. The aer is organized as follows. In Sect. 2, we resent the rotocol secification and the baclog counting rinciles. In Sect. 3, the framewor of the analytical aroach is described. Sect. 4 resents the analysis of results for the saturation erformance. In Sect. 5, the simulative validation of the analytical results is given. 2 Protocol Secification The LonTal/EIA acet cycle consists of two hases (Fig. 1). The first hase is otional and dedicated to riority messages. During the other hase nodes randomize their access to the medium. Since the goal of our analysis is the redictive - CSMA, we assume that there are no riority slots in the acet cycle.

3 2.1 LonTal/EIA Pacet Cycle The redictive -CSMA belongs to the slotted-csma algorithms where the time axis is slit into segments called slots with the duration equal to β 2. β β 1 2 Pacet Fig. 1. LonTal acet cycle Priority slots (0-127) Randomizing window ( slots) Pacet The algorithm oerates in the following way. A node attemting to transmit monitors the state of the channel. If the channel is busy the node continues sensing. When the node detects no transmission during the β 1 eriod, it delays a random number of time slots of β 2 duration. If the channel is still idle when the random delay exires, the node transmits. Otherwise, the node receives an incoming acet and cometes for the channel access again. If more than one node choose the same slot, and when that slot is the earliest one among the slots selected by all the contending nodes, then a collision haens. All the acets involved in a collision are corruted. The time by which the cometing node defers the transmission is exressed as a seudorandom number of time slots β 2 drawn from the uniform distribution between 0 and W, where W is the size of the randomizing (cometition) window. The size of the randomizing window is dynamically adjusted to the current channel load. If the channel is idle, the randomizing window consists of 16 time slots. When the channel load increases, the number of slots grows by factor BL, called the estimated channel baclog. The baclog BL can range from 1 to 63 and the size of the window varies from 16 to 1008 time slots since the following relationshi is met: W = BL (1) W base where W base is the size of the basic randomizing window (16 slots). Thus, the level of the ersistence of the redictive -CSMA has either the lower (1/16=0.0625), or the uer bound (1/1008=0.0009). 2.2 Baclog Switching Rules The baclog estimation is based on the calculation of the number of acets exected in the cometition for the channel during the next acet cycle [1]. The baclog concet relies on monitoring the information included in the header of each acet transmitted in the channel. This information, encoded in 6-bit long field Delta _ BL, reresents the number of acnowledgements that will be generated by receiver(s) as a result of acet recetion. Thus, Delta _ BL = 1 for unicast and 1 < Delta _ BL 63 for multicast messages.

4 The channel baclog BL is increased by Delta _ BL as a result of sending or successful receiving the message. Next, the baclog counter BL is decreased by one: (i) at the end of each successful acet cycle or (ii) if no node occuies the channel. If the collision detection is enabled, the baclog is increased by one in the case of collision. On a basis of the baclog counting algorithm we can conclude that after a successful transmission of the message, the baclog BL grows by ( Delta _ BL 1). Each node calculates the baclog autonomously basing on the baclog counter imlemented in the LonWors node firmware. To ee the consistency of baclog states, all nodes in the networ should modify their baclog counters in the same way. We assume that both Physical Layer and Lin Layer of rotocol do not introduce the baclog inconsistency, i.e. the channel might be assumed to be noise-free and all transceivers are able to detect collisions even if they are not senders of colliding acets. Then, the baclog is a global channel arameter. 3 System Modeling Following the definition, the saturated status of a networ is reached if each node has a acet to send. We assume that the networ consists of a fixed number of n nodes and the baclog consistency between the nodes is et. 3.1 Analytical Model of Channel Baclog Let BL n ( l) be a stochastic rocess reresenting the baclog stage at the lth acet cycle in a networ consisting of n nodes, where BL n ( l) = 1,..., 63. As it was stated, we assume that the rocess BL n ( l) is a global measure of the channel. BL n ( l) is the Marov chain with transition robabilities n i, j, i, j = 1,...,63. The first goal of our analysis is to find a stationary distribution of baclog π = [ π ], = 1,..., 63. Next, the saturation baclog BL is calculated as the exected baclog in the long term: BLmax BL = E[ BL ( l )] = π = 1 where E[ ] is the exectation oerator. The saturation window is defined as the mean size of the randomizing window in the saturation conditions: W = 16BL We assume the load scenario called ACK/unicast in short, where all the acets sent through the networ use the acnowledged service and unicast addressing. Thus, after each acet recetion, a receiving node generates a single acnowledgement. In such a scenario we distinguish three tyes of acet cycles (see Sect. 2.2): (1) an (2) (3)

5 unsuccessful transmission due to the collision, which causes the channel baclog BL to increase by one in the next acet cycle: BL ( l + 1) = BL ( l) + 1, (2) a successful transmission of the unicast message, when the channel baclog BL does not change: BL ( l + 1) = BL ( l), and (3) a successful transmission of the acnowledgement which decreases the baclog BL by one: BL ( l + 1) = BL ( l) 1. The ey assumtion in our model is that robabilities of the successful transmission of the acnowledgement and the message are the same. The validity of this assumtion will be checed in Sect. 5. According to this assumtion, if the robability ( of a collision at a certain baclog stage BL n ) ( l) = with n cometing nodes amounts to, then both the robabilities of a successful transmission of a message and an acnowledgement equal (1 ) 2. Suose that the baclog enters the stage at the lth acet cycle, i.e. ( BL n ) ( l) =. Let Pr { BL ( l + 1) = + s BL ( l) = } =, + s be the transition robability that the baclog enters the stage ( + s) in the (l+1)th acet cycle from the stage in the lth cycle. Taing the secification of the acet cycle tyes (1)-(3) into account and baclog limits we calculate the robabilities of switching between baclog stages:, 1 = Pr { BL ( l + 1) = + 1 BL ( l) = } + =, =1,..., 62 1, = Pr { BL ( l + 1) = BL ( l) = } = (1 ) 2, (1 + ) 2, = BL min = 2,...62 = BL 1 = Pr { BL ( l + 1) = 1 BL ( l) = } = (1 ) 2, = 2,..., 63 max = 1 = 63, + s = Pr { BL ( l + 1) = + s BL ( l) = } = 0, s > 1, = 1,..., 63 The diagram of the Marov chain for a given scenario is shown in Fig. 2. (1) coll 1 2 (1 (2) ) 2 (1 (2) coll (3) (61) coll (62) ) 2 (1 ) 2 (1 ) 2 (62) (63) (4) (1) 1 coll (1 (2) ) 2 (1 (62) Fig.2. The state transition diagram of the Marov chain for ACK/unicast scenario ) 2 (1 + (63) ) 2

6 3.2 Baclog Stationary Distribution In order to find the saturation baclog, the steady-state vector, or the stationary distribution π = [ π ], = 1,...,63 of the Marov chain has to be calculated. The stationary distribution π is an eigenvector of the transition matrix P, associated with the eigenvalue equal to one. The vector π = π ] includes the long-term robabilities [ π that the channel baclog will be at the stage in the steady state, that is: π = lim Pr{ BL( l) } (5) = l Using the direct method of the steady-state vector π linear equation has to be solved: i, j comutation, the following T [ G e] π = b (6) i, j where P = [ ] is a transition matrix 63 x 63; the elements are given by (4), G = P I, I is an identity matrix 63 x 63; e = e ] is a vector, where e i = 1 ; i = 1,...,63; [ G e] is 63 x 64 matrix, where the last column of this matrix is a vector e ; b = b ] is a vector, where b = 0, b + 1 = 1; i = 1,..., 63 [ i i i. [ i 3.3 Probabilities of Successful and Unsuccessful Transmission i, j In order to find we have to calculate, i.e. the robability that the transmission is in a collision if n nodes comete for the channel, and the current window consists of 16, = 1,...,63 time slots. To be recise, is the robability that more than one node selects the same time slot and all the other nodes choose later slots: n s = 1 ( ) (7) s where ( ) is the robability of a successful transmission for the window containing 16 time slots, i.e. the oosite event to collision occurrence. The robability n s ( ) describes the drawing when there is a single winner of a channel cometition and is exressed as the sum (according to all the 1,...,16 slots and 1,...,n nodes) of the following: (i) the robability that a winner selects a certain slot s = 1,..., 16 which equals 1 16, (ii) the robability that all the other ( n 1) nodes draw one from ( 16 s) later slots, which equals n 1 ((16 s) 16). Finally: s ( ) 16 n s = n s= (8)

7 Basing on the ditribution of the contention window π = π ], we can estimate the saturation robability of collision [ as the following exectation: BLmax 16 n 1 = = 1 16 s coll = 1 n π s (9) succ Hence,, the saturation robability of the successful transmission succ coll equals: = 1. 4 Saturation Channel Baclog and Probabilities Using the analytical aroach outlined in Sect. 3 we obtained the following results. The grahs resenting BL and vs. the number of nodes n for a secified load scenario (ACK/unicast) are shown in Fig. 3. Each oint on the saturation baclog grah is found as a solution of the linear system given by Eq. (6) for a articular number of nodes and the exectation (Eq. (2)). is calculated according to (9). Saturation channel baclog Saturation collision robability Saturation channel baclog Number of nodes Saturation collision robability [%] Fig.3. The saturation baclog and the saturation collision robability for ACK/unicast scenario At the lower range the saturation baclog increases almost linearly as the number of nodes grows and the sloe of the curve is about 0.06 er node. In articular, this means that adding a new node to the existing networ causes the increase of the saturation window by about 0.06*16 1 time slot of β 2 duration. For networs larger than about 700 nodes, the influence of the uer bound of the channel baclog revents a further extension of the cometition window. If a networ contains more than 1000 nodes, then the saturation baclog is close to its maximum value 63, and the redictive rotocol is reduced to the ersistent CSMA. Summing u, the rediction is effective for the networ sizes u to 700 nodes.

8 As regards the saturation collision robability, the robability grows in roortion to the number of nodes for a networ containing dozens of devices (Fig. 3). Next, becomes steady at 33,3 % for the networ sizes larger than 100 nodes. Thus, succ is et at 66,7 %. This is an imortant result for the redictive CSMA erformance. It shows that the rotocol manages to control the size of a cometition window in order to guarantee the sustained robability of successful transmission, which in the analyzed scenario equals 66,7%. The successful transmission sustained robability is the worst-case robability of successful transmission for the redictive CSMA if the rediction if effective, i.e. the current baclog is not limited by BL max = 63. Although, the effect of eeing the high throughut of the redictive CSMA has been nown [2,3,7], there has been no exlicit quantitative evaluation of sustained robability of successful/unsuccessful transmission. Note that sustained robabilities succ = 66,7% and = 33,3% are established at the equilibrium oint, when the robabilities of the baclog increase succ ( 2 ) and decrease are equal. Finally, for networs greater than 700 nodes, the influence of the maximum size of a cometition window aears, and the shae of both measures is close to that of ersistent CSMA. 5 Validation of Analytical Aroach In order to verify the analytical aroach we have erformed the simulations for a selected number of nodes in the networ saturation status. The simulation starts when the channel is idle. Next, the transient zone aears, when the nodes ermanently try to access the channel and the mean channel baclog grows, but does not reach the steady-state value. Since the simulation model belongs to non-terminating systems and the steady state theoretically is never reached, we detect it with a finite accuracy. The detection relies on the search of the constant value of the mean baclog rather than the constant value of the current baclog. Therefore, we used the moving averages defined on a window of observations (i.e. a certain number of acet cycles). Moving averages filter the higher frequency comonents in the mean baclog, arisen from the random behavior of the CSMA algorithm on the one hand, and remove also the influence of the transient zone on the estimation of the saturation baclog on the other. The saturation baclog is found under quasi steady-state conditions when the moving average of the channel baclog is et inside of 5% wide confidence interval. 5.1 Validation of Transition Probabilities The transition robabilities in the Marov model have been derived basing on the equality of the robabilities of the successful transmission of a message and an acnowledgement (see Sect. 3.1). This assumtion is true if the mean number of nodes having a message waiting for the transmission (i.e. message sources) equals the mean

9 number of nodes that ossesses an acnowledgement ready for sending (i.e. acnowledgement sources). Fig. 4 resents simulation results showing the mean relative number of message and acnowledgement sources in the networ steady state. It is clear that both numbers are equal to 50% with finite simulation accuracy. Percentage of acnowledgement and message sources [%] Mean relative number of sources of acnowledgements and messages Sources of messages Sources of acnowledgements Number of nodes Fig. 4. Simulation results of the mean relative number of message and acnowledgement sources in the steady state 5.2 Simulation versus analytical results The comarison of simulation and analytical results for the saturation baclog and the robability of collision and its exerimental equivalent (i.e. collision ercentage ' n ), is resented in Table 1. Since both results are very close to each other and the corresonding grahs overla, they are not shown in figures together. The comarison shows a good conformity of simulation and the Marov-based analytical aroach. The difference between both results stems from (i) the finite accuracy of the steady state detection in the simulation, (ii) the inaccuracy of the seudorandom generators, (iii) the finite recision of analytical calculations. Table 1. The comarison of analytical and simulation results for saturation baclog and saturation robability of collision for the ACK/unicast load scenario n BL (Marov model) BL (simulation) [%] (Marov model) ' ( n ) [%] (simulation) succ [%] (Marov model) ' ( n ) succ [%] (simulation) 2 1,128 1,124 5,56 5,77 94,44 94,23 6 1,390 1,387 13,12 13,68 86,88 86, ,663 1,661 17,49 17,98 82,51 82, ,9476 4,028 28,48 28,96 71,52 71, ,8567 8,889 31,15 31,97 68,75 68, ,634 42,160 32,89 33,3 67,11 67, ,194 61,428 42,53 42,72 57,47 57,28

10 6 Conclusions The aer resents the analytical study of the efficiency of networ load rediction built in the redictive -CSMA/CD that is used as a MAC rotocol in Lon- Wors/EIA-709 sensor/control networing technology. The aroach based on the Marov chains is alied. The rocedure of erformance analysis includes the definition of transition robabilities of the Marov chain for a secified load scenario, the calculation of stationary distribution of contention window, and the robabilities of successful/unsuccessful transmission. The analysis is exemlified on the load scenario where the acnowledged message service and unicast transactions are used. The resented results allow to recognize the redictability of the rotocol behavior in heavy load conditions. In articular, it is shown that the redictive -CSMA rotocol manages to control the size of a cometition window in order to guarantee the sustained robability of successful transmission. The simulative validation of analytical results is rovided. Further research should generalize the erformance analysis for general case load scenario. References 1. LonTal Protocol Secification, Version 3.0, Echelon Cororation (1995) 2. Enhanced Media Access Control with LonTal Protocol, LON Eng. Bull. (1995) 3. Miśowicz, M., Saor, M., Latawiec, W., Zych, M.: Performance analysis of redictive -ersistent CSMA rotocol for control networs. Proceedings of IEEE International Worsho on Factory Communication Systems WFCS'2002 (2002) Miśowicz, M.: Saturation erformance of redictive -CSMA without collision detection. Proceedings of IEEE International Conference on Emerging Technologies and Factory Automation ETFA'2005 (2005) Miśowicz M.: Send-on-delta concet: an event-based data reorting strategy. Sensors, Secial Issue: Wireless Sensor Networs and Platforms, Vol. 6 (2006) Buchholz, P., Plönnigs, J.: Analytical analysis of access-schemes of the CSMA tye. Proceedings of IEEE International Worsho on Factory Communication Systems WFCS'2004 (2004) Chen, X., Hong, G.-S.: A simulation study of the redictive -ersistent CSMA rotocol. Proceedings of 35th Annual Simulation Symosium (2002) Chen, X., Hong, G.-S.: Real-time erformance analysis of a fieldbus-based networ. Proceedings of Information, Decision and Control Conference (2002) Koetz, H.: Real-Time Systems. Design Princiles for Distributed Embedded Alications. Kluwer Academic Publications (1997) 10. Kleinroc, L., Tobagi, F. A.: Pacet switching in radio channels. I. Carrier sense multile-access modes and their throughut-delay characteristics, IEEE Transactions on Communications, Vol. COM-23, no. 12. (1975) Layer 7 LonMar Interoerability Guidelines, Version 3.2, LonMar (2002) 12. Neuron C Reference Guide, Echelon Cororation (1995)