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Average Channel Utilization of CSMA With Geometric Distribution Under Varying Workload Marek Mis´kowicz, Member, IEEE
Abstract—Performance analysis of fixed-size contention window carrier sense multiple-access (CSMA) protocol with geometric distribution for slot selection probability is addressed in the paper. This MAC scheme, called Sift, was initially proposed for large-scale event-driven wireless sensor networks. The goal of the present paper is to evaluate the standard performance measures (throughput, protocol capacity, collision rate, and mean access delay) for geometrically distributed CSMA both in the context of data-centric dense sensor networks and node-centric industrial automation systems. The analytical approach based on the stochastic analysis has been applied. To demonstrate how the protocol is able to cope with bursty traffic, the average throughput defined over a specified workload range has been introduced and examined. Using the average throughput as the performance criterion, the geometric CSMA has been compared to conventional CSMA schemes with uniform distribution. The latter are represented by the classical -persistent CSMA and the predictive -persistent CSMA used in LonWorks control networks. It is shown that G-CSMA is overload-tolerant event-driven MAC protocol since the average throughput may be kept on high level in wide range of workload if the shape of geometric distribution is well chosen. Index Terms—Access protocols, carrier sense multiaccess, communication system performance, modeling.
I. INTRODUCTION UE TO flexibility, simplicity, and robustness of random access schemes, the carrier sense multiple access (CSMA)-based protocols constitute the heart of contemporary media access control technology for wireless networking. CSMA schemes resemble the dynamics of human conversation. The basic CSMA consists in “listen before you talk” principle and was invented in the middle of the 1970s for radio communication [1]. By asking a station to listen before transmission, the CSMA scheme tries to prevent it from transmitting when other stations transmit. A successful modification of pure CSMA algorithm for wired computer networks is a version with collision detection (CSMA/CD) commercially implemented in Ethernet (IEEE 802.3). The principle of collision detection is “listen while you are talking.” Although the use of collision detection improves CSMA performance, detecting collisions during transmission is not feasible in wireless communication. A collision occurrence in a wireless channel may only be deduced by a message sender implicitly on the basis
D
Manuscript received October 04, 2008; revised January 11, 2009 and February 26, 2009. First published April 14, 2009; current version published May 06, 2009. This work was supported in part by the Polish Ministry of Scientific Research under Grant N R02 0015 04. Paper no. TII-08-10-0121.R2. The author is with the Department of Electronics, AGH University of Science and Technology, Cracow, Poland (e-mail:
[email protected]). Digital Object Identifier 10.1109/TII.2009.2017524
of a lack of an acknowledgement packet from a receiver. If a collision detection cannot be implemented, the mechanism of reducing collision occurrences is applied in the form of collision avoidance schemes. The class of CSMA protocols with collision avoidance (CSMA/CA) is dedicated mainly to wireless communication. The best known representative of CSMA/CA protocols is the IEEE 802.11 for wireless local-area networks (LANs). In wired systems, the CSMA/CA schemes can be integrated with collision detection (e.g., in LonTalk MAC scheme [2]). Furthermore, collision detection is then often used as one of collision avoidance policies by reducing the probability of successive collisions on retries. A common method of collision avoidance is to adapt a contention window size to the current number of contenders. Several techniques of tuning a number of contention slots in terms of varying network workload have been proposed and successfully applied. All of them consist in a window extension after a collision and a window size decrease in case of a successful transmission. In the class of variable-window CSMA protocols, the generic policies of window size modification consist in the binary exponential backoff or a combination of additive (linear) and multiplicative dynamic tuning of the number of slots as a response to the result of transmission attempt. For example, most protocols double the contention window after collisions using the truncated binary exponential backoff (e.g., 802.11, Ethernet). A multiplicative-increase-additive-decrease scheme has been proposed in MACAW protocol [3]. On the other hand, an additive-increase-additive-decrease scheme is used in the predictive -persistent CSMA exploited in LonWorks control network technology [2]. The alternative technique proposed recently consists in introducing a nonuniform distribution for the probability of choosing slots within the CSMA contention window of a constant size [4]. It has been proved that for a fixed number of contenders and a given contention window size, the distribution maximizing the probability of a successful transmission is exponential [4]. The finite discrete approximation of the exponential distribution, that is, the truncated geometric distribution, is more convenient to implement in pseudorandom number generators used in MAC protocols. The CSMA with the geometric distribution has been called Sift protocol and dedicated to dense event-driven wireless sensor networks [5]. In this paper, which is the extension of [6], we examine this protocol in a more general context of network architectures as initially proposed in [5]. Therefore, we refer to it using a term geometric CSMA (G-CSMA) to emphasize underlying principle that distinguishes this scheme from conventional CSMA protocols.
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II. PROTOCOL SPECIFICATION As known, in the slotted-CSMA schemes, the packet transmission is successful when a certain contending node wins the contention by selecting the earliest slot among the contenders, and when all the other nodes choose later slots.
Fig. 1. Transmission attempt according to slotted-CSMA scheme.
A. Principles of G-CSMA Scheme The proposed probability distribution for choosing a contention slot in G-CSMA is geometrically increasing, i.e., the probability of drawing a subsequent slot in the fixed-size window is multiplicatively increased in relation to a preceding slot [4], [5]. As a result, usually most contending nodes select late slots, and merely a few nodes choose one of early slots. In this way, the true contention is reduced to these nodes that draw initial slots even if the total number of contenders is in the order of hundreds or thousands. This greatly reduces the probability of collision. For example, as will be further shown, by selecting the appropriate shape of geometric distribution, the probability of successful transmission might be kept around 0.8 even if 100 nodes compete only for 16 contention slots. The contention resolution defined by the G-CSMA can be integrated in various protocols that involve random network access (e.g., sift has been adopted in Crankshaft protocol for sensor networks [7]). However, until now, no CSMA scheme with the geometrical distribution has been commercially implemented in a network platform. B. Performance Analysis Profile As mentioned, the G-CSMA/Sift protocol has been invented for large-scale data-driven wireless sensor networks based on the event-based architecture. In [8], the term extensive sensor networks (ESNs) has been proposed to refer to this class of systems. In ESNs, a certain event is usually reported by multiple sensor nodes which results in spatially correlated contention (i.e., correlation between traffic produced by the nodes located in the same geographical area). Thus, in the ESNs, not all nodes have to send their reports to higher level protocols since only a subset of individual reports is needed. Therefore, on the MAC layer top, the ESNs use event-to-sink protocols as reliable transport schemes. In the complementary network architecture defined as intensive sensor/control networks (ISNs), an event of interest in a sensor field is usually reported by a single node only [8]. Consequently, a reliable end-to-end delivery of data packets has to be provided at the Transport Protocol according to the assumption that each packet carries unique, significant, and nonredundant information. The objective of the ISNs design is to optimize network performance, especially to maximize the channel utilization. On the other hand, all aspects of ESNs operation, including MAC protocols, are focused on efficient energy management. The representative examples of ISNs are event-driven fieldbus networks like CAN or LonWorks. Thus, the ISNs are closer to industry or to building automation networked systems rather than to densely deployed data-centric wireless sensor networks with spatiallycorrelated contention. However, the difference between ISNs
and ESNs does not consist in application areas but in distinct architectures. For the scope of this paper, the difference in the range of network workload between ISNs and ESNs is important. The population of contending nodes in ESNs may vary by one, two, or even three orders of magnitude in a short time. Instead, in a normal type of the operation of ISNs, the traffic is relatively low, and increased in some overload situations (e.g., when a burst of events occurs). Usually, in the peak load, the number of contenders in ISNs is not higher than a few nodes. We discuss the G-CSMA performance analysis in the context of workload characteristic both for ESNs and for ISNs. The contribution of this paper is twofold. First, we carry out systematic performance analysis of the slotted-CSMA with geometric distribution in terms of throughput/delay characteristics. The analytical approach is applied. Second, we compare the G-CSMA to the predictive -persistent CSMA protocol using the average throughput defined for a specified workload range. To keep consistency of the analysis, we have selected the same performance measures as in [9] and [10] for the predictive -persistent CSMA and as in [11] for the pure -persistent CSMA in order to compare corresponding results. C. G-CSMA Specification We assume a slotted-CSMA algorithm where the time axis is split into segments, called contention slots whose duration is equal to . The algorithm operates in the following way. A node attempting 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 period, it delays a random number of time slots of duration (Fig. 1). If the channel is still idle when the random delay expires, the node transmits. Otherwise, the node receives an incoming packet and competes for the channel access again. If more than one node choose the same slot, and where that slot has the lowest number selected by any contending node, then a collision happens. All the packets involved in a collision are corrupted. The random delay (backoff) is expressed as a pseudorandom number of the time slots of duration drawn from the truncated is the size geometric distribution between 1 and , where of the contention window. The geometric distribution is skewed giving preference towards slots located at the end of the window. Summing up, in the G-CSMA as in the other slotted-CSMA schemes, the access to the shared channel is organized in packet cycles. Each packet cycle is an attempt of a packet transmission undertaken by node(s) that has data ready for sending. A packet cycle begins with an interpacket space and a random number followed by a packet transmission of empty contention slots (Fig. 1). The result of each transmission attempt is a successful
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MIS´KOWICZ: AVERAGE CHANNEL UTILIZATION OF CSMA WITH GEOMETRIC DISTRIBUTION UNDER VARYING WORKLOAD
transmission of a packet or a collision. The mean lengths of sucand unsuccessful packet cycles are funccessful tions of the number of contending nodes, , and are defined as follows:
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TABLE I PDFS OF CHOOSING SLOTS WITHIN CONTENTION WINDOW
(1) (2) denotes the mean slot number when a sucwhere cessful transmission starts, represents the mean is the length slot number when a collision occurs, and or of transmitted packets. The components define the mean number of empty slots preceding (successful or unsuccessful) packet transmission. If the colliding packets have different lengths denoted by , , then , , and is the number of colliding where packets. D. G-CSMA Versus IEEE 802.11 The difference between the G-CSMA and the IEEE 802.11 is that the former belongs to the fixed-window CSMA protocols like the -persistent CSMA, and the IEEE 802.11 is the representative for variable-window schemes like the predictive -persistent CSMA. Furthermore, the backoff timer is memoryless in the G-CSMA, i.e., the contenders draw backoff times in every transmission attempt anew and cancel them when the transmission is detected in the channel. In the IEEE 802.11, the nonmemoryless backoff is applied where the competing nodes freeze their backoff timers in case of detecting transmission, wait to the end of the current packet transmission, and then resume these timers [12]. E. Shape of Geometric Distribution In the analyzed G-CSMA, the probability of selection of a certain slot increases with the slot number as follows [5]:
in the window. For simplicity, we refer to the CSMA with the uniform distribution as to the special case of . the G-CSMA, where F. Optimal Shape of Geometric Distribution The optimal shape of the geometric distribution maximizing the probability of successful transmission and defined by is selected for the number of contenders , and for the window is approximated by the following formula [5]: size . The
(3) ; is a characteristic coefficient where that determines the shape of the probability distribution. The formula (3) is obtained as a result of normalizing to one the truncated geometric distribution defined by parameter. The probability is increased slowly for initial slots and grows rapidly for final slots. If the distribution parameter is small, the is concentrated in the very last slot. Then, the number of contenders picking one of initial slots is drastically limited resulting in minimizing the probability of collision. In Table I, the probability density functions of choosing conand different values of are pretention slots for sented. Note that if , then each of the initial 13 slots is selected with probabilities less than 5% and the very last slot , the may be found is chosen with 60% chance. If , so the truncated geoby the asymptotic limit metric distribution converges towards the uniform distribution. This limit corresponds to the conventional -persistent CSMA with the uniform distribution where for each slot
(4) The plots of for according to (4) in Fig. 2. For example, if and of optimal values narrows with the growing
are presented slots, then . The range .
III. ANALYTICAL MODEL OF G-CSMA A. Network Model In our analysis, we suppose the following assumptions for the protocol settings and the traffic model. We assume that a network is in the saturation status, that is, the system consists of a constant number of contending nodes, , that always have packets ready to be sent. The channel is assumed to be noise[bits] free. Next, we suppose that the interpacket space is [bits], and all the long, the contention slot width equals packets transmitted via the channel are of constant length denoted by and equal to 96 [bits]. These settings are consistent with those used in the model of the -persistent CSMA in [11],
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C. Analytical Formulae for Performance Measures and be, respectively, the mean number Let of successful and unsuccessful transmissions per time unit. Next, let BR denote the channel bit rate. It is clear that (6) and (7) According to the definition, the throughput , and the collision rate CR normalized to the channel bit rate BR are given by (8) Fig. 2. Optimal value of versus number of nodes for W
= f16; 32; 48g.
and the predictive -persistent CSMA in [9]. It is also assumed that the contention window size in the G-CSMA consists of 16 slots as the basic contention window in the predictive -persistent CSMA [2].
(9) Setting (5)–(7) to (8) and (9), we obtain the following formulae for the channel throughput and the collision rate:
(10)
B. Definition of Performance Measures To evaluate the G-CSMA performance, we use the principal measures for random access networks: throughput, protocol capacity, collision rate, and mean access delay. There is no unique definition for channel throughput. We use a definition of the throughput as a fraction of time used for successful transmissions of packets in a channel [13]. We express the throughput as a percentage of the channel bit rate. Such a throughput definition corresponds to the mean channel utilization. The protocol capacity is the maximum achievable throughput. The collision rate is defined as the fraction of time during which the transmitted packets are involved in collisions [13]. The mean access delay is defined as an average time from the instant a node starts trying to send a packet until the beginning of its successful transmission [13]. of sucThe difference between the probabilities cessful/unsuccessful packet transmission, and the throughput/ collision rate, respectively, consists in that the former measures define which fraction of all packet cycles in network steady state is successful/unsuccessful, and the latter specify which fraction of channel bandwidth is dedicated to successful/unsuccessful and , throughput and transmissions. Therefore, unlike collision rate take into account: — distinct lengths of successful and unsuccessful packet cycles (on the average the latter is longer than the former, see Figs. 4 and 5); — a fraction of bandwidth, wasted during the channel compeand the number of empty tition (i.e., interpacket space before the start of each transmission). slots As known (5) but the sum of throughput and collision rate is less than one.
(11) The protocol capacity
is given by the definition (12)
The mean access delay
may be found as (13)
where is the expected number of attempts undertaken by a given node to send a packet successfully and (14) represents the mean length of a packet cycle in the channel access [10]. As the transmission attempts are independent and may be modeled by a geometric distribution, the expected number of trials until the first success is the inverse of the probability of a success at any trial that equals (15) Finally, by setting (14) and (15) into (13), we obtain (16) The analytical model represented by (10)–(12), and (16) is exact provided that a network is at the steady-state saturation status and a channel is noise-free. The formulae (10)–(12) and (16) are valid for any slotted-CSMA protocol with memoryless backoff. These formulae were used in [9] and [10] for the performance evaluation of the predictive -persistent CSMA. How-
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ever, the corresponding analyses were already reported in earlier works [14], [15] although sometimes with a different terminology convention. In particular, the channel throughput defined by (10) corresponds to the mean channel utilization in [14], and the mean access delay expressed by (5) agrees with the waiting time in [14]. The present paper is thus an extension of previous works [9], [10], [14], and [15], addressing the performance analysis of CSMA schemes with memoryless backoff. As follows from (10)–(12) and (16), all final measures deand given by (1) and (2). On the other pend on and are functions of because and hand, both depend on . Summing up, to compute , , , , the following intermediate measures have to be evaluated: , or — probability of successful transmission ; — mean slot numbers and . In the forthcoming section, we will present an analytical ap, , proach to compute the intermediate measures , against the number of contenders, , for the G-CSMA. To simplify the notation, we often refer to the corresponding parameters in short ( , , , , etc.) without an explicit indication that they are functions of . D. Stochastic Analysis of G-CSMA
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Fig. 3. Probability of successful transmission versus number of nodes.
Next, the mean slot number when the successful transmission starts is found by the following expectation: (21) is a conditional probability that a transmiswhere sion starts in the th slot provided that the transmission attempt is successful. when a collision occurs Similarly, the mean slot number
In the G-CSMA with defined by (1), the probability of successful transmission (of any node) in the slot , is given by the following expression [12]: (17)
(22)
where , is given by (3). The probability is calculated as the probability that any node selects the slot , nodes do not choose any slot from the and all the other , multiplied by a number of nodes, . range of Furthermore, the collision probability in the slot [12]
is a conditional probability of collision in slot where provided that the transmission attempt is unsuccessful. The is defined for since a collision may happen only if more than one node compete for channel access. for In particular, by substituting the probability to (17)–(22), we obtain the correeach slot sponding formulae for the conventional fixed-window CSMA that are used first in [14], with uniform distribution [15] , and then in [9] and [10]. Thus, (17)–(22) are the generalizations of the performance measures for the slotted-CSMA with any slot probability distribution and memoryless backoff.
(18) where is the binomial coefficient that counts a number of combinations of elements from the set of elements. The probability is found by summing the . probabilities that nodes collide in the slot for For a given , the latter probability corresponds to the number of combinations where subsets of nodes select the (same) slot , and the other nodes do not choose slots from 1 to . Finally, the probability of a successful transmission (in any slot) may be computed as (19) and the (total) probability of collision
might be found by (20)
IV. G-CSMA PERFORMANCE ANALYSIS In Figs. 3–9, the plots of the corresponding G-CSMA performance measures according to the analytical approach specified in Sections III-C–III-D are presented. All the measures are computed versus the number of contending nodes for selected to values of the distribution parameter varying from . As a reference for the G-CSMA, we use the CSMA . protocol with the uniform distribution Analyzing the shapes of the plots in Figs. 3–9, we can conclude that two components, in general, influence the CSMA performance: the collisions, and the waste of bandwidth due to randomizing the uncoordinated channel access. The collisions are the primary component of dropping the channel utilization
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Fig. 4. Mean slot number where successful transmission starts.
Fig. 7. Collision rate versus number of nodes.
Fig. 5. Mean slot number where collision happens versus number of nodes.
Fig. 8. Mean access delay versus number of nodes.
Fig. 6. Throughput versus number of nodes.
f16
under high contention. Then, frequent or even excessive colliand the throughput . On the other hand, sions degrade the the empty slots (defined by ) preceding a packet transmission are a main reason of waste of bandwidth under low contention (Fig. 1). The throughput maximization (i.e., protocol capacity) corresponds to the optimal population of contenders for which both effects balance (see Figs. 3, 4, and 6).
; 32; 48
Fig. 9. G-CSMA protocol capacity versus number of nodes for g.
W =
A. Analysis of Collisions and Empty Slots In Fig. 3, the plot of the is presented. The is a decreasing function of for . However, for , is a function that has a single maximum for the opthe timal number of contenders defined by (4). This is a new feature of the CSMA protocol obtained in the G-CSMA in result of introducing the increasing nonuniform slot distribution.
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As shown in Figs. 4 and 5, the and the are strictly decreasing functions of . As mentioned, for the small is a dominant (suboptimal) number of contenders , component of the bandwidth waste. In particular, so the mean number of empty slots and nearly equal to half of the window size. is for for any It can also be proved that number of nodes since the collisions are more likely in and later slots. Under high contention, both approach one asymptotically. Moreover, for a given , the and the increase with decreasing . Thus, the average number of empty slots preceding both successful and unsuccessful packet transmission is unfortunately longer and grows with decreasing . This is a price for keeping a low probability of collision for large in the G-CSMA. B. Analysis of Throughput and Collision Rate The G-CSMA throughput versus the number of active contenders for a given is a function that has a single maximum as (Fig. 6). This maxfor the conventional CSMA with imum corresponds to the protocol capacity . The workload maximizing the does not match exactly the workload max(compare Figs. 3 and 6). imizing the , both the and the throughput decrease For rapidly with a growing , as seen in Figs. 3 and 6, which is a well-known disadvantage of the CSMA with uniform distribution. For small , the throughput plots become flatter, which causes the maximum throughput to be close to the average throughput defined over a wide range of the number of nodes, , the throughput is quasi-constant up to 100 e.g., if contending nodes. For a large number of nodes, the throughput provides a good approximation of the since (23) Then, by simplifying (1) and (2) (24) Finally, using (24) as the approximation of (1) and (2) in (10) and (11), we obtain simplified expressions for the throughput and the collision rate that are more accurate for a large : and . C. Analysis of Mean Access Delay The plot of the mean access delay versus the population of contenders is depicted in Fig. 8. For small , the mean access delay is determined by empty slots preceding successful grows with decreasing transmissions. Since the (Fig. 4), the mean access delay for a small number of contenders is slightly longer for the G-CSMA compared with the conventional CSMA. If is large, the dominant component of access delay is the probability of successful transmission of a ). This probability decreases with single node (equal to (a large and still) growing due to two factors. The first reason because of excessive collisions. is the decrease of the The second reason is the decrease of the fraction of channel bandwidth available per node because the total bandwidth is divided among the growing number of contenders .
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Using the approximation (24) in (16), which is valid for a can be approximated by large number of nodes, (25) As follows from (25), for the range of where the is quasi-constant (see Fig. 3), the mean access delay grows almost linearly with the increasing number of nodes (Fig. 8). D. Analysis of G-CSMA Protocol Capacity Optimizing the G-CSMA for ESNs usually consists in maximizing the probability of successful transmission since primary objective of the ESNs design is to reduce power consumption (as known, collisions are more energy-expensive than empty slots in CSMA schemes). That problem was discussed in Section II-F. On the other hand, the goal of optimal shaping the geometric distribution in ISNs is to maximize channel utilization. This problem will be examined now. As stated, the G-CSMA throughput for a given reaches its maximum equal to the protocol capacity for a certain number of contending nodes. A comparison of Figs. 3 and 6 for a given shows that the number of contenders maximizing the does not match exactly the number of active nodes corresponding to the protocol capacity. This is because the throughput maximization corresponds to the optimal number of contenders for which waste of bandwidth due to collisions and empty slots balance (see Section IV-B). is shown. In Fig. 9, the plot of the protocol capacity Each point on this plot corresponds to the maximum achievable throughput for a given . Thus, the G-CSMA capacity constitutes an upper limit for channel utilization with a selected . As seen in Fig. 9, the shape of depends on . For slots, the G-CSMA capacity is decreasing with a growing . is much greater, the protocol capacity is maxiHowever, if mized for a certain number of contenders. The plot in Fig. 9 is a throughput of a hypothetical G-CSMA is tuned dynamically with the current protocol where the number of contenders to reach protocol capacity. Thus, the shows potential characteristics of the protocol capacity channel utilization of a dynamic G-CSMA protocol. V. COMPARISON OF PROTOCOLS AVERAGE THROUGHPUT As shown in Fig. 6, the G-CSMA throughput varies with changing workload and reaches its maximum for a preselected number of contending nodes. The next interesting problem is to examine how stable the protocol throughput is under bursty traffic. We introduce the average throughput as a parameter that represents a network performance in varying load conditions and we define it for a range of 1 to contenders (26) where is given by (10). We assume by convention that the maximum number of contenders is not higher than ten nodes in ISNs, and than 100 nodes in ESNs. Consequently, we define and as the measures representative for average channel utilizations in ISNs and ESNs, respectively.
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TABLE II COMPARISON OF G-CSMA AND PREDICTIVE p-PERSISTENT CSMA IN TERM OF AVERAGE THROUGHPUT
Fig. 10. Throughput of predictive p-persistent CSMA versus number of contenders for various load scenarios [9].
The definition stated by (26) represents the average throughput accurately if the channel load varies slowly (i.e., under the assumption of the quasi-static load evolution). With a rapidly varying number of stations, the model of (26) is only an approximation of real average throughput since the network may not necessarily reach the steady-state in the meantime. Similarly, we define the average G-CSMA protocol capacity (27) where
is the capacity for a number of active nodes.
A. Average Throughput of G-CSMA and for seIn Table II, the numerical results of lected values are listed against the average G-CSMA protocol and that constitute the capacities and . upper limits for is high (0.7 As seen in Table II, for large values, the ), but is unsatisfactory (below 0.5 or more if ). For , both and are if kept on a high level (greater than or equal to 0.7). At the same is characterized by time, the conventional CSMA with and by very low (equal to 0.24). With a good high selection of , the G-CSMA outperforms the pure -persistent CSMA as regards the average throughput both in the range of , and . Due to a high performance in wide range of workload, the G-CSMA can be recognized as an overload-tolerant event-driven MAC protocol. Summing up, by selecting the appropriate shape of the distribution, the user can achieve a satisfying G-CSMA performance close to the average capacity in the range of an expected channel load. B. Average Throughput of Predictive -Persistent CSMA Now, we will compare the G-CSMA to the predictive -persistent CSMA in terms of an average channel utilization. Both
the G-CSMA and the predictive -CSMA use a memoryless backoff. Furthermore, the predictive -CSMA is characterized by high throughput for heavy channel load, and is commercially implemented in LonTalk/ANSI/CEA-709.1-B protocol in tens of millions of LonWorks devices. The plots of the throughput versus the number of active nodes for the predictive -CSMA with collision detection cited from [9] are presented in Fig. 10. We have selected the protocol version with the collision detection since it provides better performance compared with the version of the predictive -CSMA without the collision detection. Since the performance of the predictive -CSMA (unlike the -CSMA and the G-CSMA) depends on the structure of the traffic transmitted via the channel, representative load scenarios with homogeneous input traffic are considered as follows: unacknowledged message service with no acknowledgements (UNACKs), acknowledged message service with unicast messages (ACK/unicast), and acknowledged service with messages addressed to a group of two recipients and the (ACK/multicast(2) (Fig. 10). In Table II, the for particular load scenarios of the predictive -CSMA are listed. Average throughputs for messages are listed below the corresponding throughputs for any packet types. As seen in and of the G-CSMA are close to Table II, both those of the predictive -CSMA for load scenario with multicast messages. However, as reported in [16], the high channel utilization in the predictive -CSMA is obtained at cost of minimizing fraction of bandwidth used for the transmission of messages carrying application data. In other words, if average throughput of the predictive -CSMA is high (e.g., 0.78 and 0.7 for ACK/multicast(2), respectively), most packets transmitted are acknowledgements (e.g., average throughputs for messages are 0.26 and 0.23 only). Moreover, the adaptation mechanism in the predictive -CSMA introduces unfairness among the nodes especially if no collision detection is provided [9]. Instead, the high G-CSMA average throughput is attained without any limitations on the traffic structure transmitted via the channel. Thus, as opposed to the predictive -CSMA, high G-CSMA average throughput is obtained regardless of packet
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MIS´KOWICZ: AVERAGE CHANNEL UTILIZATION OF CSMA WITH GEOMETRIC DISTRIBUTION UNDER VARYING WORKLOAD
types transmitted. Furthermore, due to extreme algorithm simplicity, the network access according to G-CSMA is fair. VI. CONCLUSION The G-CSMA performance analysis shows that this scheme is a powerful solution both in the context of large-scale datacentric sensor networks, and of industrial automation systems. Due to a high performance in a wide range of workload, the G-CSMA is an overload-tolerant event-driven MAC protocol. By introducing a geometric distribution to a CSMA scheme, new perspectives arise for the effective MAC protocols design. Natural ideas are to implement in the G-CSMA adaptive mechanisms complementary to those used in conventional CSMA algorithms. The first suggestion is to make a common parameter variable and dependent on other network measures. The other idea is to introduce priorities by differentiating values among the contenders. In the latter, a higher can be assigned to contender(s) with higher priority to increase the probability of choosing early slots. In such a protocol, the will become a node-specific parameter in contrast to the (static is common for all the or dynamic) G-CSMA, where the nodes in the network.
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[5] K. Jamieson, H. Balakrishnan, and Y. Tay, “Sift: A MAC protocol for event-driven wireless sensor networks,” MIT, Cambridge, MA, Tech. Rep. LCS-TR-894, 2003. [6] M. Mis´kowicz, “Performance analysis of slotted-CSMA with geometric distribution,” in Proc. IEEE Intern. Workshop Factory Comm. Syst., WFCS’2008, 2008, pp. 21–29. [7] G. P. Halkes and K. G. Langendoen, “Crankshaft: An energy-efficient MAC-protocol for dense wireless sensor networks,” in Proc. Eur. Conf. Wireless Sensor Netw., EWSN’2007, 2007, pp. 228–244. [8] M. Mis´kowicz, “Comparison of intensive and extensive sensor networking technologies,” Int. J. Online Engineering, vol. 1, no. 2, pp. 1–5, 2006. [9] M. Mis´kowicz, “A generalized analytic approach to the evaluation of predictive p-CSMA/CD saturation performance,” in Proc. IEEE Intern. Workshop on Factory Comm. Syst., WFCS’2006, 2006, pp. 342–352. [10] M. Mis´kowicz, “Analysis of mean access delay in variable-window CSMA,” Sensors, vol. 7, no. 12, pp. 3535–59, 2007. [11] M. Mis´kowicz, “On the capacity of p-persistent CSMA,” Int. J. Comput. Sci. Netw. Security, vol. 7, no. 11, pp. 38–43, 2006. [12] A. Warrier and I. Rhee, “Stochastic analysis of wireless sensor network MAC protocols,” North Carolina State Univ., Comput. Sci. Dept., Raleigh, NC, Tech. Rep., 2005. [13] J. Yeh, “Simulation of local computer networks – A case study,” Comput. Netw., vol. 3, pp. 401–417, 1979. [14] P. Buchholz and J. Plönnigs, “Analytical analysis of access-schemes of the CSMA type,” in Proc. IEEE Int. Workshop on Factory Commun. Syst., WFCS’2004, 2004, pp. 127–136. [15] P. Koopman, “Tracking down lost messages and system failures,” Embedded Systems Programming, vol. 9, no. 11, pp. 38–52, 1996. [16] M. Mis´kowicz, “Limits of performance of adaptive variable-window CSMA,” in Proc. IFAC Int. Conf. Fieldbuses Netw. Ind. Embedded Syst., FeT’2007, 2007, pp. 239–244.
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Marek Mis´kowicz (M’03) received the M.S. and Ph.D. degrees in electronic engineering from AGH University of Science and Technology (AGH-UST), Krakow, Poland, in 1995 and 2004, respectively. He is currently an Assistant Professor in the Department of Electronics, AGH-UST. His research interests include performance analysis of networked sensor and control systems, event-based sampling, and asynchronous analog-to-digital conversion.
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