On Achieving Fairness and Efficiency in High-Speed Shared Medium Access

Transcription

1 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 11, NO. 1, FEBRUARY On Achieving Fairness and Efficiency in High-Speed Shared Medium Access R. Srinivasan, Member, IEEE, and Arun K. Somani, Fellow, IEEE Abstract Channel access has been an active research area for the past two decades. Several protocols have been proposed in literature to efficiently utilize the channel bandwidth. Some of the recently proposed protocols achieve a near-ideal channel utilization. However, the efficiency in utilization comes at the expense of certain unfairness in delay characteristics. In this paper, a new channel-access protocol, called access mechanism for efficient sharing in broadcast medium networks (AMES-BM), is developed based on a deterministic binary tree-splitting technique to achieve efficient sharing of bandwidth. In AMES-BM, the stations are dynamically mapped to leaf nodes of a binary tree. The stations are then divided into smaller groups that mimic the behavior of an ideal transmission queue. Collisions are allowed to occur within these groups and are resolved using a variation of the conventional binary tree-splitting technique. The performance of AMES-BM is similar to that of a collisionbased protocol under low loads and to that of a collision-free protocol under high loads. Besides achieving a near-optimal channel utilization, the proposed protocol also guarantees fairness with respect to delay for messages of varying lengths. The deterministic nature of the protocol makes it more attractive for real-time applications. Index Terms Broadcast networks, collision resolution, multiple access, tree splitting. I. INTRODUCTION CONSIDER a set of stations that share a single-channel communication medium. The stations communicate with each other by sending messages over the shared channel. Only one station can transmit a message successfully at any given time. When more than one station tries to use the channel, a collision is said to occur and the messages are lost. Investigating the methods of utilizing the channel efficiently has been an active research area for the past two decades. The channel-access protocols can be broadly classified into two categories: collision-free and collision-based protocols. Time-division multiple-access (TDMA), where the channel is divided into time slots and every station is assigned an unique slot, is an example of a collision-free protocol, while ALOHA, carrier sense multiple access (CSMA), and carrier sense multiple access with collision detection (CSMA/CD) are examples Manuscript received November 13, 2000; revised January 13, 2002, June 9, 2002, and June 30, 2002; approved by IEEE/ACM TRANSACTIONS ON NETWORKING Editor T. Todd. This work was supported by the David C. Nicholas Professorship of Electrical and Computer Engineering at Iowa State University. R. Srinivasan is with the Department of Electrical and Computer Engineering, University of Arizona, Tucson, AZ USA ( srini@ece.arizona.edu). A. K. Somani is with the Department of Electrical and Computer Engineering, Iowa State University, Ames, IA USA ( arun@iastate.edu). Digital Object Identifier /TNET of collision-based protocols. Collision-based protocols utilize the channel efficiently under low loads while the throughput reduces drastically at high loads due to an increase in the number of collisions. Collision-free protocols, on the other hand, work well under high loads but underutilize the channel bandwidth under low loads resulting in larger delays. Collision-free protocols such as TDMA are effective under uniform traffic that require a constant bandwidth like voice transmission. Data traffic on the other hand are typically bursty in nature. Several variations of protocols have been proposed to enhance the network utilization under bursty traffic scenario. Reservation ALOHA (R-ALOHA) [1] is one such protocol that divides the channel bandwidth into slot sizes equal to the transmission time of a single packet of fixed length. The channel access is divided into frames comprising of slots. A station that transmits successfully in a slot of a frame retains the slot in the next frame. Stations contend for unused slots in a frame using Slotted ALOHA. Variations of this protocol includes ability of a station to transmit in multiple slots in a frame, thereby taking advantage of the unused bandwidth. However, these approaches use random backoff procedures in case of collisions, thereby resulting in poor channel utilization under low loads and unfairness in the bandwidth allocated to different stations. For a detailed report on the variations of R-ALOHA, see [2]. An efficient way to achieve a good utilization both at low and high loads is to dynamically allocate the channel bandwidth to the contending stations by resolving collisions. Tree splitting was one of the first techniques proposed for collision resolution. When a collision occurs, the colliding stations are split into groups, 0 through. Stations present in group 0 are allowed to transmit, followed by stations in group 1, 2, and so on. If a collision occurs in a group, then second-level groups are created. The above procedure is used recursively until all the collisions are resolved. For, the technique is called binary tree-splitting. The tree-splitting technique could be based on probabilistic or deterministic methods. In probabilistic methods, the stations choose to be part of a group at random, while in deterministic approach, the stations are assigned unique identifiers and the collisions are resolved using these identifiers. Capetanakis [3] proposed the first protocol based on binary tree-splitting using probabilistic approach that achieved a maximum throughput of The protocol was improved by Massey [4] to achieve a maximum throughput of Gallager [5] and Tsybakov and Mikhailov [6] showed that a channel feedback could be used efficiently to improve the throughput. A near-ideal channel utilization was shown to be achievable in [7] if the number of stations involved in a /03$ IEEE

2 112 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 11, NO. 1, FEBRUARY 2003 collision is known. Protocols proposed with this assumption in [8] [10] achieved a throughput of only The upper bound on the maximum achievable throughput using data packets for collision resolution with ternary feedback model has been shown to be [11]. An increase in utilization beyond is achieved by some protocols using control minislots (CMS) [12] [17]. The control minislots are much smaller in length compared to a data slot. Among them, the distributed queueing random-access protocol (DQRAP)[17] achieves the best performance. The minislots are much smaller in size compared to the data packets, thus, minimizing the loss upon a collision. The protocol divides the channel access into slots. Every slot has control minislots and one data slot. Two distributed queues, one for transmitting requests and the other for transmitting data, are used to achieve performance equivalent to that of the hypothetical perfect scheduling protocol (M/D/1). It has also been shown that with the use of three CMSs per slot, the protocol is stable for all offered loads up to one. This protocol also led to the evolution of the cable-tv protocol, IEEE , which uses a ternary tree-splitting technique with -persistence [22], [23]. If a centralized channel arbitrator is not used, then the duration of a minislot has to be at least equal to the round-trip time in the network. The probabilistic approach to resolve collisions has two inherent limitations. First, the protocols are unstable if the offered load exceeds a certain threshold, resulting in a drastic reduction in the throughput. Second, the network delay is unbounded, making these protocols not suitable for real-time applications. A deterministic approach to tree-splitting could be employed to overcome the above two problems. Among several protocols that have been developed based on deterministic binary-tree splitting [18] [21], incremental collision resolution multiple access (ICRMA) has been shown to be the best. The collisions are resolved using control packets that are much smaller than the data packets. The protocol uses a transmission queue to achieve a near-optimal channel utilization, but increases the average packet delay for shorter messages. The goal of this paper is to develop an efficient deterministic channel-access protocol for broadcast network shared by bursty stations that ensures fairness to messages of varying length while maintaining a near-optimal channel utilization. The paper is organized as follows. Section II describes the system model. Section III describes in detail the limitations of ICRMA. The working of deterministic binary tree-splitting algorithm is analyzed and the avenues for performance improvement are detailed in Section IV. Using this analysis, we develop a new channel-access protocol in Section V. The performance of the protocol is studied using extensive simulation for various network scenario. The performance results are discussed in Section VI. The conclusions are presented in Section VII. II. SYSTEM MODEL Consider a system with up to stations connected through a single shared communication channel. It is assumed that every station in the network can listen to every other station. The channel access is assumed to be slotted for ease of explanation. The application of the protocol for an unslotted channel is described in Section VI-E. A slot is the basic unit of transmission and all the stations are synchronized to slot boundaries. The stations monitor the channel continuously and obtain a feedback about the channel status that indicates whether a slot is idle, has a collision, or is used for a successful transmission. The feedback is obtained within the slot duration, hence the duration of a slot is at least equal to the round-trip time in the network. A message to be transmitted by a station is made up of several packets. Each packet transmission extends over multiple slots. All the packets are of fixed length and require slots for transmission. A station starts transmission at the beginning of a slot boundary, and transmits one packet if no collision occurs. When a collision is detected, the station aborts transmission. Hence, only one slot of information is lost. As every packet transmission needs to be followed by an idle period of duration at least equal to the maximum one-way propagation time in the network, we fix the slot duration as 1.5 times the round-trip time in the network. It is assumed that there are no failures in the system and all the stations have a consistent view of the channel at any given time. III. MOTIVATION Among the protocols discussed in Section I, three protocols, DQRAP, IEEE , and ICRMA, are of particular interest as they have been shown to achieve a near-optimal channel utilization. The ICRMA protocol uses a deterministic collision resolution algorithm, while DQRAP and IEEE employ a probabilistic method. The average number of collision resolution steps required to resolve a contention in ICRMA is smaller than that in DQRAP [21]. Hence, the wastage due to ICRMA is lower than that of DQRAP. As IEEE also employs a ternary tree-splitting technique similar to DQRAP, the above result applies to the cable-tv protocol as well. These properties make the ICRMA protocol a good candidate for the system considered in this paper. ICRMA uses control packets for collision resolution. However, as the stations are assumed to have the capability to abort transmission upon collision detection, a recommended change would be to use the data packets directly for channel access. A. MICRMA for a Slotted Broadcast Channel The ICRMA protocol [21] divides the channel access into cycles. Each cycle has a short contention period (one slot) followed by a collision-free transmission period. Stations, that are not already in the transmission queue but have a message, transmit a packet during the contention slot. If no collision occurs, the station continues with the packet transmission. The station enters the transmission queue if it has more packets to transmit. If a collision is detected, the contending stations abort transmission. The collision is resolved using a deterministic binary tree-splitting technique (explained in detail in Section IV) in the future contention slots. During the transmission period, the stations in the queue transmit a packet each. When transmitting a packet, the station informs if it is going to leave the queue or not after the transmission. The protocol with these modifications will, henceforth, be referred to as MICRMA.

3 SRINIVASAN AND SOMANI: FAIRNESS AND EFFICIENCY IN HIGH-SPEED SHARED MEDIUM ACCESS 113 first packet. As shown in Fig. 1, S1 transmits two packets before S3 could transmit its first packet. This phenomenon occurs frequently at high loads, resulting in a larger delay to enter the transmission queue. Once the station enters the transmission queue, the packets are transmitted with smaller delay, leading to a bias in favor of longer messages. This bias, at high loads, is independent of the transmission speed of the network. To overcome this deficiency, it is necessary to ensure that no station in the network transmits more than one packet unless all the stations that have a packet to transmit get their chance to transmit. Fig. 1. Working of the MICRMA protocol. Fig. 1 shows the working of the MICRMA for a slotted channel. Initially, the transmission queue is empty. Station S1 transmits successfully in the contention slot and enters the transmission queue during cycle. During cycle, no other station has a message to transmit. Hence, the contention slot is idle. Stations S2 and S3 contend during cycle and result in a collision. Station S2 and S3 enter the transmission queue in cycles and, respectively. Although the protocol achieves a near-optimal channel utilization, it still has certain limitations as illustrated by the following example. Consider a network with a round-trip time of 54 s. The average message length is ten packets, with a packet size of 53 bytes. The slot duration is 81 s. Therefore, at 1 Mb/s a packet extends over approximately five slots. B. Effect of Contention Slot at Low Loads The contention slots are mostly idle at low loads and unnecessarily increase the delay in the network. For example, consider a situation where only one station has a message of length ten packets to transmit. It takes ten cycles for the station to transmit the message, and nine slots are wasted as contention slots (one in each cycle following the transmission of the first packet). An extra delay of nine slots is seen by the message. This delay is not significant at low transmission speeds as the packet transmission time is larger than the slot time. In the above example, a one-slot delay for packet transmission amounts to a 20% increase in delay. If the transmission speed of the stations increases to 8 Mb/s, a packet can be transmitted within a slot duration. Hence, the extra delay amounts to almost a 100% increase in the delay. In this case, the maximum bandwidth seen by any station is half of the utilizable channel bandwidth. Obviously, it is not desirable to have a contention slot for every cycle. C. Effect of Contention Slot at High Loads At high loads, a different phenomenon takes place. A new station that wants to transmit a message contends to enter the transmission queue. It takes several cycles for a contending station to enter the transmission queue, as only one collision resolution step is carried out in each cycle. The stations that are already present in the transmission queue get to transmit more than one packet before a contending station could transmit its D. Effect of Transmission Queue Size ICRMA fixes the maximum size of the transmission queue. If the maximum queue size is less than the total number of stations in the system, then the issue of when a station should leave the queue needs to be addressed. The stations can be allowed to remain in the queue as long as they have a packet to transmit. In such a case, the maximum achievable throughput is determined by the maximum queue size. If denotes the maximum queue size, then the maximum achievable throughput is. However, employing one collision resolution per cycle increases in the initial delay for a station to enter the transmission queue due to larger number of stations in the transmission queue. Also, if the maximum queue size is smaller than the total number of stations, it would result in starvation under certain traffic conditions. Hence, the maximum queue length for the above condition of leaving the transmission queue should be the maximum number of stations in the system. If the stations leave the transmission queue after every message transmission to overcome starvation, then the maximum achievable throughput is directly affected by the average number of packets in a message. For example, consider a system where the probability that a station that is in the transmission queue leaves the queue in a cycle with a probability (assuming that the average packet length is and the probability of a message termination is independent from one cycle to another). As not more than one station can enter the transmission queue in a cycle, the maximum input rate to the queue is restricted to one station per cycle. Hence, at steady state, the average number of stations in the queue is. If the maximum queue size queue is more than, the maximum achievable utilization is. Therefore, as the message length decreases, the maximum achievable throughput decreases. For example discussed earlier, each packet extends over five slots when the transmission speed is 1 Mb/s. With an average message length of ten packets, the maximum achievable utilization is However, if the transmission speed is increased to 8 Mb/s, each packet occupies a timeslot. Hence, the maximum achievable utilization drops to 0.9. Increasing the transmission speed further would enable more data to be fit in a timeslot reducing the average message length. If the average message length is five, then the maximum achievable throughput further drops to In the MICRMA protocol considered in this paper, it is assumed that the stations are allowed to remain in the queue as long as they have a message to transmit.

4 114 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 11, NO. 1, FEBRUARY 2003 E. Effect of Number of Active Stations The performance of MICRMA also depends on the number of stations present in the system at any given time, and the size of the binary tree that is used to resolve collision. In a system that can have a maximum of 128 stations, a binary tree with 128 leaf nodes is required to resolve collisions. However, if only four stations are active at one time, it is sufficient to have a binary tree with four leaf nodes. A static mapping of the stations to the binary tree will not be adaptive to the variation in the number of active stations in the system. It is preferred that only the active stations form the binary tree so that the wastage due to collisions is minimized. F. Fairness With Respect to Message Length Network applications generate data of varying lengths. The data is divided into a number of segments as it passes through the lower layers of the network protocols. While some of them fit within a packet, the others extend over multiple packets. Typically, applications that transmit voice have data that fit within a packet. Other applications, such as video and file transfer, have data extending over multiple packets. As the lowest granularity of access to the network is through a packet, the channel-access protocols should provide a fair access for the different stations in the network at the smallest granularity. The working of the MICRMA, as explained in the example earlier, has an inherent bias toward longer messages. The channel access to the stations is more like an ON OFF model where the bandwidth availability is more than the average during the ON period with no access to the channel during OFF period. These observations motivate us to analyze the binary treesplitting technique. To start with, we consider a system where every station implements a deterministic version of the binary tree splitting. The binary tree-splitting technique is analyzed for the minimum number of collision and idle slots that are required to resolve a contention. This analysis leads to developing a new channel-access protocol in a systematic manner. IV. DETERMINISTIC BINARY TREE-SPLITTING ALGORITHM Every station in the system has a unique physical identifier, where. Each station is also a unique leaf node of a -level binary tree. Hence,. The leaf nodes are numbered from 0 to. The stations are arranged on the tree using a virtual identifier, denoted by, rather than using the physical identifier. The collisions are resolved using the virtual identifiers. Each station has a stack that holds identifier intervals, denoted by (, ). The top of the stack entry is the allowable interval. Stations whose virtual identifier lie within this allowable interval are permitted to transmit in the next contention slot. Upon a collision, the allowable interval is split into two subintervals, and, and they replace the top entry in the stack. Depending on which of the two subintervals is pushed last on the stack, the priority is decided. In this paper, it is assumed that the right subtree is given priority over the left subtree. Therefore, the lower subinterval is pushed first on the stack followed by Fig. 2. Three-level binary tree for eight stations. the higher subinterval. When a successful transmission 1 or an idle slot is observed, the allowable interval is popped from the stack. When the stack becomes empty, the interval is pushed back onto the stack. The time (in slots) between two successive insertions of interval is defined as a binary tree-split cycle (BTScycle). A. Example Consider a system with eight stations, with virtual identifiers 0 to 7. The arrangement of the stations in a binary tree is shown in Fig. 2. Suppose that stations 1, 6, and 7 have messages to transmit. The stack is initialized with interval (0, 7). The tree-splitting algorithm proceeds as follows. 1) Stations 1, 6, and 7 transmit, resulting in a collision. The allowable interval is split into two subintervals (0, 3) and (4, 7). The allowable interval for the next contention slot is (4, 7). 2) Stations 6 and 7 transmit and collide again. The allowable interval is further split into two subintervals (4, 5) and (6, 7). The interval (6, 7) is the allowable interval for the next contention slot. 3) Stations 6 and 7 transmit and collide again, resulting in further split of the allowable interval. The stack after the end of this step has the subintervals (0, 3), (4, 5), (6, 6), and (7, 7). 4) Station 7 transmits successfully. The interval (7, 7) is popped out. 5) Station 6 transmits successfully. The interval (6, 6) is popped out. 6) The slot for the interval (4, 5) goes idle. The interval (4, 5) is popped out. 7) Station 1 transmits successfully and the interval (0, 3) is popped out. This marks the end of BTS-cycle and stack is reinitialized with interval (0, 7). Thus, the BTS-cycle had three collision slots, three successful transmissions ( slots), and one idle slot. All the stations execute the above algorithm regardless of whether they have a packet to transmit or not. In this algorithm, the stations that are part of the stacked entries are allowed to join the collision resolution when a BTS-cycle is in progress. For example, if a message arrives at station 4 when Step 2) of the algorithm is in 1 A successful transmission lasts for L slots. However, the stack operation is carried out only for the first successful slot and no stack operations are performed for the following L 0 1 slots.

5 SRINIVASAN AND SOMANI: FAIRNESS AND EFFICIENCY IN HIGH-SPEED SHARED MEDIUM ACCESS 115 progress, it is allowed to participate for channel access in Step 6). In such a case, the total number of contending stations is considered to be four, instead of three. B. Analysis Let denote the number of contending stations in a BTS-cycle. Let,,, and denote the number of collision slots, number of idle contention slots, number of successful transmissions, 2 and total number of wasted slots in a cycle, respectively, to resolve a contention involving stations mapped uniquely to the leaf nodes of a -level binary tree. Theorem 1: The minimum number of collision steps required to resolve a contention with the deterministic binary tree-splitting technique involving stations mapped uniquely to the leaf nodes of a -level binary tree is lower bounded by., for. Proof: The theorem is proved using induction. The validity of the above theorem can be checked for and for all. Let the theorem be true for any and such that, i.e.,. It remains to be shown that the theorem holds true for and, such that, i.e.,, where. This is shown using the first step analysis. If or, there is no collision,. Hence, the theorem is true. If, then there is a collision at level 0. Let and denote the number of nodes that are located in the left and right subtree, respectively. and satisfy and At level 1, the left and right subtrees are two independent -level binary trees. Therefore, it follows that If either or (when ), (1) reduces to If both and are nonzero, we have The lower bound for the number of collision slots required to resolve a contention involving stations is independent of the number of levels in the tree. However, not all collisions involving stations can be resolved in exactly steps. If it can be done, then such an arrangement of stations is called an optimal arrangement. The following theorem shows the existence of optimal arrangement for a contention involving stations. Theorem 2: Given contending stations, there exists an arrangement on a -level binary tree, where, such that the contention is resolved with exactly collisions. 2 S(k; m) denotes the total number of successful transmissions (not the successful transmission slots). Hence, S(k; m)=m for all cycles. (1) Proof: The theorem is proved by showing that there exists an algorithm, for all and, to arrange stations in a -level binary tree in an optimal way. It can be verified that exists for all, as the station can be assigned to any one of the nodes. The existence of for is shown through recursive proof. If, then there is a collision at the root node (Level 0). Let and denote the number of stations assigned to the left and right subtree, respectively. As a collision is already encountered, the contention on the left and the right subtree needs to be resolved in exactly steps. If (or ), then (or ). But by Theorem 1, the contention involving stations cannot be resolved in steps. Therefore, and should be nonzero. The existence of and can be shown along similar lines, as exists for all. Hence, exists for all and. The excess collision slots required to resolve a collision due to contending stations, denoted by, is defined as. Moreover, every excess collision slot has an associated idle contention slot. Hence, every BTS-cycle obeys the equation. Thus, the total number of slots wasted to resolve a collision due to contending stations can be written as From the above equation, it is observed that there are three possibilities for performance improvement. Reducing excess collision slots: As every excess collision slot has an associated idle slot, it is possible to remove an excess collision slot upon experiencing an idle slot. For example, if there is a collision at the root node, and the contention slot corresponding to the right subtree is idle, then the contention slot corresponding to the left subtree would result in an excess collision, which could be avoided. This improvement would reduce the wastage by at most. Reducing idle contention slots: Although every excess collision slot has an associated idle slot, a collision slot cannot be classified as an excess collision slot unless its corresponding idle slot is seen, as the number of contending stations is not known until the end of the BTScycle. While reducing idle slots implies reducing excess collision slots, the converse is not true. Hence, the only possible way of reducing idle slots is to arrange the stations optimally on the binary tree. Reducing necessary collisions: The necessary collision slots cannot be reduced if the basic binary tree-splitting technique is used. It can be reduced if the BTS-cycle is started at some intermediate level instead of starting at the topmost level. However, this may increase the idle slots during a collision resolution. V. PROPOSED PROTOCOL: AMES-BM In this section, we develop a new channel-access scheme. The channel access is divided into a sequence of BTS-cycles. The schedule for the next cycle is constructed deterministically by observing the current cycle.

6 116 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 11, NO. 1, FEBRUARY 2003 Define a continuing station as one that transmits a packet successfully in the current cycle and also has a packet to transmit in the following cycle. The first step to construct a schedule for the following cycle is to count the number of continuing stations. This is achieved by having a flag in every transmitted packet to identify a continuing station, denoted by. A station that has a packet to transmit for the next cycle sets the flag in the packet that it transmits in the current cycle. Every station maintains a variable to count the number of continuing stations in the current cycle. When a successful transmission with the flag set is observed, the stations increment the number of continuing stations by one. The value of at the end of the current cycle provides the number of contending stations for the next cycle. With this information, the schedule for the next cycle is constructed in three steps. 1) Dynamic node mapping:given stations that continue to the next cycle, the first step is to arrange them optimally on a -level binary tree. This step is aimed at avoiding the excess collision slots during collision resolution. 2) Dynamic grouping: To avoid the collisions that are caused due to the conventional binary tree-splitting approach, the system is dynamically divided into groups. The channel access is also divided into intervals and each group is assigned an interval. The stations are grouped in such a manner that each group has exactly one continuing station. 3) Dynamic collision resolution: Given that the next cycle has been optimally arranged for continuing stations, new stations that have a message to transmit are allowed to contend for channel access within one of the groups. The resulting collisions are resolved using a variation of the conventional binary tree-splitting technique. A. Dynamic Node Mapping The node mapping procedure is to arrange stations on a -level binary tree, such that a contention involving these stations can be resolved in exactly steps. The proof of Theorem 2 in Section IV-B provides a generic mechanism to arrange stations in a -level binary tree optimally. A special case of the optimal arrangement is to arrange stations such that the number of stations in the left and right subtree rooted by any intermediate node does not differ by more than one, i.e., defining and in the algorithm. In such a case, all the subtrees rooted by nodes at level have exactly one or no continuing stations. Let the continuing stations of the current cycle be re-numbered from 0 to. The reversed string of the -bit binary representation of numbers from 0 to have a unique property. If the continuing stations are mapped to the leaf nodes corresponding to the reversed binary string of their numbers, then their collisions can be resolved optimally. It can be observed that such a mapping also leads to the special case mentioned above. In the example considered in Section IV-A, if stations 1, 6, and 7 are renumbered as 000, 001, and 010, then they would occupy node positions 000, 100, and 010, respectively, in the next cycle using the reversed binary strings. TABLE I CHANGES IN lrt AS THE CURRENT CYCLE PROCEEDS This property is used to assign dynamic node mapping to the stations. All stations maintain a variable that indicates how recently that station transmitted in the current cycle. The stations assign their s as the reversed -bit binary representation of their current value, at the beginning of every cycle. The cycle is carried out with this and it remains unchanged until the end of the cycle, although the value of can change during the cycle. A station transmits its current value of along with every packet, denoted by. If the flag is set, the station that transmitted the packet sets its as 0, while all the other stations with less than increment their value by one. If the flag is not set in the transmitted packet, the values are not updated. Consider the example discussed in Section IV-A again. Without loss of generality, assume that the of every station is the same as its at the beginning of the current cycle. The of every station should, therefore, be the reversed binary representation of its. Table I shows the changes in values of the stations as the cycle proceeds. The values in the first row are the binary reversed value of the (also their ) values of the stations. The number that is underlined in each row denotes the value transmitted by the station with its packet. The numbers shown in bold face in each row denotes the stations whose is incremented due to the successful transmission. The cycle ends after the successful transmission of Station 1. The values for the next cycle are assigned as the reversed binary values of the in the last row of the table. B. Dynamic Grouping To reduce the collisions caused due to the conventional binary tree-splitting technique, the tree is split into smaller subtrees before starting the next cycle. A possible approach to split is to start the next cycle at level. This divides the tree into groups, with nodes in each group. However, this may introduce some idle slots. Another possibility would be to split at level. However, this may introduce some collision slots, as each group may be occupied by more than one continuing station. Depending on which level results in lesser wastage, the tree could be divided accordingly. For the example discussed earlier, the following cycle can start from level 1 or 2. In both cases, either one collision slot or one idle slot is wasted. Fig. 3(a) shows the grouping of stations if the tree is split at level 1 and 2. The dotted squares in the figure show the grouping at level 1 and the ellipses show the grouping at level 2.

7 SRINIVASAN AND SOMANI: FAIRNESS AND EFFICIENCY IN HIGH-SPEED SHARED MEDIUM ACCESS 117 Fig. 3. Different ways of grouping stations for the next cycle. (a) Splitting the tree at a particular level. (b) Splitting the tree at multiple levels (mimics a transmission queue). To avoid collision and idle slots, the tree can be split into exactly binary subtrees. In this approach some groups have nodes, while the remaining groups have nodes. For the example discussed in Section IV-A, if stations 1, 6, and 7 have multiple packets to transmit, they would occupy nodes 0, 4, and 2, respectively, on the binary tree at the end of the current cycle. The tree is divided into three subtrees. The corresponding subintervals denoted by (0, 1), (2, 3), and (4, 7). The stack is initialized with these intervals, with (4, 7) being the next allowable interval. It can be observed that the leftmost node in the interval is always occupied by a continuing station from the current cycle. This exact grouping of stations mimics the behavior of an ideal transmission queue. Fig. 3(b) shows the dynamic grouping. C. Dynamic Collision Resolution The above two steps ensure that the next cycle is optimally arranged for continuing stations. Next, we discuss how new stations that have messages to transmit join a BTS-cycle. Every subinterval in the stack at the beginning of the cycle is a binary tree. Hence, the binary tree-splitting technique (as described in Section IV) could be used to resolve new collisions arising within groups. However, this would be inefficient. In the example discussed above, consider a scenario when a station with (in the next cycle) in the range 5 7 has a message. This results in a collision corresponding to the interval (4, 7). If the conventional tree-splitting is followed, the station with would also contend, resulting in an increase in the average number of collision resolution steps. Such collisions could be avoided by removing the continuing stations from participating in collision resolution. To achieve this, a variation of the treesplitting technique is employed. The representation of an interval that is stored in the stack is modified to a 3-tuple, denoted by (,, ). The variable is allowed to take two values, or, which indicates whether the interval is used for transmission or collision resolution, respectively. If there are no continuing stations, the stack is initialized for the next cycle with the interval (0,, ). Otherwise, the of all the intervals that are pushed onto the stack before beginning a cycle are set to. Every station also maintains a status variable,, that denotes the state of a station at any given time. All the continuing stations in the current cycle set their values as for the next cycle. If a station that transmits in the current cycle is not a continuing station, then it sets its value as. A message arrival takes a station from state to state. It can be observed that for every interval (,, ), the station that occupies node should have, and all other stations occupying nodes from to will have or, unless there are no continuing stations in the current cycle. When the allowable interval is (,, ), all the stations whose virtual identifiers that lie within the allowable interval are permitted to transmit, irrespective of the state of the station. This could result in a collision. Upon a collision, the allowable interval is split into (,, ), an exclusive transmission slot for the station occupying node, and (,, ), the next allowable interval that is used for collision resolution. The interval for collision resolution is given higher priority, hence is the next allowable interval. When the allowable interval is (,, ), only those stations whose identifiers lie within the above interval and are permitted to transmit. Upon a collision, the conventional binary tree-splitting is followed. The allowable interval is split into and. In the example discussed earlier, the second cycle will start with intervals (0, 1, ), (2, 3, ), and (4, 7, ) in the stack. Stations 1, 6, and 7 will have, while all the other stations will have their. When a message arrives at station 2 just before the beginning of the next cycle. Station 2 enters the state. A collision is experienced in the first slot of the following cycle as stations 2 and 6 transmit a packet. The allowable interval is split into (4, 4, ) and (4, 7, ). Station 2 transmits in the slot corresponding to interval (4, 7, ) followed by transmission by station 6 in the slot corresponding to interval (4, 4, ). D. Addition/Deletion of a Station A station that wants to leave the system (when the station is shut down) does so by transmitting a control packet, called an exit-notifier packet. The flag is not set in the exit-notifier packet. On receiving an exit-notifier packet, every station that has value greater than the value transmitted by the leaving station decrements their value by one. A station that wants to join the system (for example, when shut down and then powered up later) should have a consistent

8 118 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 11, NO. 1, FEBRUARY 2003 Fig. 4. State transition diagram for stations. view of the system before it can start transmitting messages. A stack that is consistent with other stations in the system and a unique are required to have a consistent view of the system. The following three parameters are required to create a consistent stack. : The number of continuing stations from the previous cycle to the current cycle determines the number of initial intervals in the stack for the current cycle. (,, ): Allowable interval needs to be known to identify the stack position in the current cycle. : To identify the initial splitting of the tree for the next cycle, the joining station should also know the number of continuing stations seen in the current cycle so far. As the station enters when a cycle in progress, the station could have missed some of the successful transmissions. In the proposed protocol, these parameters are transmitted along with each packet. Hence, a joining station needs to wait for one successful transmission to have a consistent view of the system. However, if no stations are currently active, idle slots would be observed. A sequence of consecutive idle slots confirms that no other station in the system is active. Recall that denotes the number of levels in the binary tree. Hence, at the end of th idle slot, the new station can initialize the stack to (0,, ). The joining station sets its initial as, hence, assigning also as. It can be observed from the dynamic node mapping algorithm that the node will be occupied only if all stations are present in the system. The joining station sends a notifier message after seeing a consistent view of the system. The notifier message should be made of at least two packets. The first packet is transmitted with the flag set. Upon successful transmission of the first packet, the value of the stations are updated, ensuring that node will remain unoccupied. If more than one station wants to join the system in a cycle, then a collision will occur corresponding to the exclusive slot in which a station with can transmit. These collisions are resolved using a random backoff scheme as these events are not likely to occur frequently. The startup procedure can be divided into two states, STP1 and STP2. A station that wants to join the system enters state TABLE II VARIABLES USED BY STATIONS STP1. The station enters STP2 when a consistent view of the system is obtained. The station tries to send the notifier message. Upon successful transmission of the first packet of the notifier message, it enters state. The stations do not accept any messages for transmission until it exits the startup phase. E. Putting It All Together Table II shows all the variables that are maintained by a station, along with their description and range of values. Among these variables,,,,,, and are transmitted as part of every packet. The state transitions for a station, as discussed in Sections V-C and D, are shown in Fig. 4. Fig. 5 shows the procedures executed by the stations. Procedure initialize gives the initialization steps for a station before beginning a BTS-cycle. The steps for transmitting a packet are shown in procedure transmit. Procedure listen shows the collision resolution algorithm that is carried out by stations. The steps involved in the startup phase is listed in procedure startup.

9 SRINIVASAN AND SOMANI: FAIRNESS AND EFFICIENCY IN HIGH-SPEED SHARED MEDIUM ACCESS 119 by the stations using first-in-first-out (FIFO) policy. For modified ICRMA, the maximum queue size was set to 32. Each point in the performance graph is obtained by averaging results over ten simulation runs, simulating ten million message arrivals for each run, to obtain a 95% confidence interval within 5% of the average value. B. Performance Metrics The performance metrics of interest are the slot utilization efficiency and the average delay. The slot utilization efficiency is measured as the ratio of the number of slots used for successful transmission to the total number of slots within a given time interval. The normalized average excess delay experienced by a packet in the system is computed as a measure of fairness. It is computed as the ratio of the delay (excluding the transmission delay) in transmitting a message to the number of packets in the message, normalized to the packet length. If denotes the number of messages of length, denotes the time at which the last packet of message is transmitted, denotes the arrival time of the message, then the normalized delay experienced by a packet that forms a message of length is given by For any given load, a constant value of with varying shows that the protocol is fair with respect to the message length. Fig. 5. Procedures executed by the stations. VI. PERFORMANCE ANALYSIS The performance of the proposed protocol and that of modified ICRMA, as described in Section III-A, has been studied using extensive simulation for various network scenarios. A. Simulation Environment A network with 128 stations has been simulated. A seven-level binary tree is used for collision resolution. The messages have a Poisson arrival rate of (per slot) for every station, and the number of packets in a message has been assumed to be geometrically distributed with mean. The total offered load to the system, denoted by, is given by. The network is simulated with a slot as the basic unit of time. The message arrival times are rounded off to the next slot boundary. The increase in average delay of a message by half a slot caused by this error is neglected. The messages are serviced C. Simulation Results Fig. 6 shows the slot utilization efficiency of AMES-BM and MICRMA for a network with packet lengths of five slots and one slot, respectively, with an average message length of ten packets. It can be observed that both protocols achieve a near-optimal channel utilization. The protocols showed similar results when the average message length was set to five packets. 3 Figs. 7 and 8 show the normalized average delay experienced by a packet with varying message lengths for and, respectively. Figs. 7(a), 7(b), 8(a), and 8(b) show the normalized average packet delay for a network with. Figs. 7(c), 7(d), 8(c), and 8(d) show the average normalized delay for a network with. It can be observed that the delay experienced at low loads is smaller in AMES-BM than that of MICRMA as the idle contention slots are avoided. Also, the difference in the delay for longer messages corresponds to, indicating the wastage of one slot dedicated for contention resolution in ICRMA. At high loads, the normalized average delay seen in the proposed protocol remains almost a constant for messages of varying lengths. This is because the protocol ensures that no station can transmit more than one packet when all the stations that have a packet to transmit get their chance. From Fig. 7, the decreasing nature of with increasing for MICRMA at high loads, indicating the bias in favor of longer messages, can 3 The channel utilization graphs for the case of P =5are not shown separately as they are identical to Fig. 6.

10 120 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 11, NO. 1, FEBRUARY 2003 (a) (b) Fig. 6. Slot utilization efficiency versus offered load for network with P =10. (a) L =5. (b) L =1. be observed for all packet lengths. As packet length (in slots) is a measure of transmission speed, it can be concluded that this bias is independent of the transmission speed. The MICRMA protocol has also been simulated with a maximum transmission queue size of 128. At loads very close to one, an 8% decrease in the average packet delay was observed compared to that experienced when the queue size was 32. As the offered load increases to one, both protocols show a similar decreasing characteristic for with increasing. This is because both protocols allocate the channel bandwidth equally among the stations. However, the queueing of messages at individual stations affects the delay experienced by the messages. As the messages are serviced in FIFO order, a smaller message waits until a longer message that is ahead of it is serviced. However, if a fair allocation of the available bandwidth is assigned to the messages by individual stations, this bias can be overcome even at high loads. D. Maximum Achievable Bandwidth The protocols are evaluated for maximum achievable throughput as seen by stations that generate messages of a certain length. The nodes are divided into groups of equal size, numbered 1. A node in group generates messages with packets in them. Once a message is transmitted successfully, a new message is generated at the next time slot. When the last packet of a message is transmitted, no new packets are in the queue. Therefore, every station has to contend for every new message. It is easy to see that the delay seen by a message is inversely proportional to the bandwidth seen by the node and directly proportional to the message length. It is to be noted that under this traffic scenario, the maximum queue length of the transmission queue in the MICRMA protocol would have any impact as long as the maximum queue length is greater than the maximum message length. The bandwidth seen by stations transmitting messages of different lengths are shown in Fig. 9(a) and (b) when the number of groups are set as 8 and 16, respectively. The bandwidth unit is measured in the unit of a packet transmission time. Hence, the bandwidth of the channel is 1. It is observed that the proposed scheme achieves fairness in bandwidth sharing as compared to ICRMA. The bandwidth seen by a node generating messages of packets is approximately 16 times that seen by a node generating single-packet messages. Under an ideal protocol, each node should have a share of of the bandwidth. However, some bandwidth is wasted due to collisions. It is observed that wastage is reduced when the data lost due to collision is less. The fairness in the bandwidth usage comes at the expense of slightly reduced overall throughput. The overall utilization for different packets sizes (in slots) are shown in Table III. The penalty in utilization is observed to be less than 10% for the cases considered. The performance of AMES-BM has also been studied with increasing the number of levels in the binary tree used for collision resolution. It is not surprising that the slot utilization efficiency and the delay characteristics have been found to be insensitive to the number of levels in the binary tree. It is observed in the simulation that the maximum number of stations that have a packet to transmit within a group is either one (the continuing station) or, at most, two (with one contending station). This implies that an increase in the degree of the collision tree (like ternary or quaternary) is not necessary.