Scheduling Algorithm for Hard Real-Time Communication in Demand Priority Network

Transcription

1 Scheduling Algorithm for Hard Real-Time Communication in Demand Priority Network Taewoong Kim, Heonshik Shin, and Naehyuck Chang Department of Computer Engineering Seoul National University, Seoul , Korea Phone: , Fax: Abstract This paper addresses the problem of scheduling periodic messages in demand priority network standardized by IEEE Committee. As regards the real-time property of the demand priority network, unnecessary blocking time due to its round-robin-based MAC protocol may cause periodic messages to miss their hard deadlines and result in low schedulability of periodic messages. We propose a new message scheduling algorithm to enforce a priority-based preemptive message transmission on the frame basis. Before a node transmits a periodic message, it broadcasts the priority of message for all nodes to construct a networkwide ready queue in order of priority. A node can transmit a periodic message only when its message is at the head of the ready queue. We have derived sufficient and necessary conditions for both static and dynamic priority assignment in order to determine the schedulability of periodic messages. The simulation study shows that the proposed algorithm significantly improves the guarantee ratio of periodic messages. 1 Introduction Distributed computer systems are widely used to support real-time applications. The timely delivery of messages over the network is essential to such systems. Messages may be dichotomized into two classes: periodic and aperiodic. Periodic messages are generated at regular intervals and must be delivered within their hard deadlines. The consequence of missing hard deadlines causes a system crash or loss of profit. Aperiodic messages irregularly arise from the external events. They are generally assumed to have soft deadlines, because aperiodic messages with hard deadlines can be modeled into periodic messages. This paper mainly deals with the problem of scheduling periodic messages in demand priority network. The demand priority network is the standard approved by IEEE committee[7, 8, 14]. It is also known as 1VG-Any-LAN and supports 1 Mbps transmission speed. Unlike Ethernet, demand priority network has a collision-free medium access control mechanism. A repeater 1 centrally arbitrates the requests from the nodes connected to it. The arbitration of repeater is based on simple round robin polling. Gaining the opportunity of access to the network, the node can transmit only one frame at a time. When the node completes the transmission of a frame, it cannot transmit another frame until the other nodes with pending frames have transmitted a frame once. Demand priority MAC protocol supports two priority levels: high and normal. High priority frames are always serviced before normal priority frames. Thus, high priority frames are applicable to real-time messages, while normal priority frames are used to deliver nonreal-time traffic such as electronic mail, file transfer, and so on. Previous works in demand priority network have focused on the support for multimedia applications such as video conferencing[3, 6, 9, 14]. The TTT(target transmission time) mechanism in [3, 14] supports a centralized bandwidth allocation. TTT represents the period over which all nodes can transmit high priority frames up to their allocated bandwidth. However, this scheme is not appropriate to hard real-time communication. Because all the time-constrained messages are treated at one priority level, i.e., high priority, bandwidth allocation scheme cannot effectively support the multiple priority levels required by the timing constraints of messages. Moreover, a short amount of TTT results in low schedulability of messages. In [6], Martini and Ottensmeyer evaluated the performance of demand priority protocol with multimedia traffic and showed that the demand priority network outperforms FDDI and DQDB. But the hard real-time traffic is not included in their analysis. They also proposed 1 In some literature, it is also termed a hub.

2 the burst mode which allows more than one frame per network access[9]. In this paper we propose a frame-based preemptive message scheduling algorithm for periodic messages to effectively support multiple priority levels of messages. In this scheme, high priority frames are used to deliver periodic messages, while normal priority frames are used to deliver aperiodic messages or nonreal-time traffic. Each periodic message consists of multiple frames and has its own priority. The round robin polling may cause the lower priority messages to block high priority periodic messages unnecessarily. The proposed message scheduling algorithm enforces the frame transmission based on the priority of messages to bound the unnecessary blocking time. The priorities assigned to periodic messages may be static or dynamic. For each priority assignment, the schedulability condition of periodic messages is analyzed and shown to be sufficient and necessary. The rest of this paper is organized as follows: Section 2 describes the operation of demand priority MAC protocol. Section 3 defines the model of periodic messages and analyzes demand priority MAC protocol to show its limitations of hard real-time communication. Section 4 proposes our priority-driven message scheduling algorithm and analyzes the schedulability condition based on priority assignment. Section 5 evaluates the performance of the proposed scheduling algorithm. The paper concludes with Section 6. Demand priority network can transmit IEEE 82.3(Ethernet) or 82.5(token ring) frame. At any instant, only one format of frame is allowed to be transmitted. Demand priority MAC protocol enables frames to be transmitted at one of two priorities: high or normal. All high priority frames are serviced before normal priority frames. However, high priority frames cannot preempt the normal priority frame currently being transmitted. In this case, high priority frames should wait until the completion of normal priority frame transmission. Figure 1 represents the sequence of signals exchanged between nodes and a repeater. Before transmitting a frame, a node first sends a request signal to the repeater. At request time, a node notifies the repeater of the priority of the frame by sending a REQ H or REQ N signal. The repeater arbitrates among all requests using a prioritized round robin polling algorithm. At each priority level, the requests are serviced in round robin order. After round robin polling, the repeater sends a Grant signal to the selected node and an Incoming signal to the other nodes. The node which has received a Grant signal begins the transmission of one frame. The repeater examines the destination address within the frame to determine the destination node and forwards the frame to that node only and sends an signal to the remaining nodes. However, multicast and broadcast frames are forwarded to multiple or all nodes. 2 Demand priority MAC protocol Node 1 REQ_H f2 REQ_N f6 A single segment of demand priority network consists of a repeater and the nodes as shown in Figure 1. The repeater in demand priority network controls the access to the network as well as regenerates the signals from one side of network to the other side. A repeater has N down-link ports where one down-link port is required for each end node. Node 2 Node 3 Node 4 f1 REQ_N REQ_N REQ_H f3 f4 f5 high priority frame REQ_H REQ_H f7 f8 time normal priority frame Figure 2. Example of prioritized round robin order Req... Src Node Dest Frame... Src Node Dest Frame (a) (c) Req Incoming... Src Node Dest Grant (b) Incoming... Src Node Dest Figure 1. The demand priority MAC protocol (d) Figure 2 shows the detailed operations of prioritized round robin polling of the repeater. Each node i is connected to the down-link port i of the repeater. Eight frames are transmitted in order of f 1 ;f 2 ;:::;f 8, while a sequence of the corresponding requests is f 1 ;f 5 ;f 2 ;f 3 ;f 4 ;f 6 ;f 8 ;f 7. The repeater maintains the two port pointers, which keep track of the last port number granted, at each priority level. Round robin polling starts at the next port to the port pointer. In Figure 2, normal priority frames f 3 and f 5 are delayed by high priority frame f 2. Upon completion of transmission of f 2, there are two pending normal priority requests. Because the port pointer at normal priority level

3 indicates port 2, the repeater begins the polling from port 3. Although the request for f 5 arrives earlier than that for f 3, f 3 is transmitted first based on round robin polling. A similar situation occurs when high priority frames f 7 and f 8 are serviced. To prevent the overload of high priority frames from causing normal priority frames to starve, normal priority frames are elevated to high priority when a specified time, called promotion time, has elapsed from their request time. A repeater can have one up-link port which may be connected to the down-link port of another repeater on a higher level. By using the up-link port, multiple repeaters can be connected to form a single network logically. As shown in Figure 3, the cascaded network has a tree structure. A root repeater controls the access to the entire network. The labels of nodes in Figure 3 represent round robin order. Node 1 Level 2 Node 2 Node 3 Level 1 Node 5 Node 6 Node 4 Root Level 1 Node 7 Node 8 Figure 3. Cascaded network with multiple repeaters 3 System model 3.1 Notations There exists a set of periodic messages M = fm 1 ;M 2 ;:::;M N g in the system comprised of N nodes. M i denotes a periodic message generated at node i. M i is characterized by (F i ; ) where F i and denote the numberofframes=d the length of a message the maximum length of a frame e and the period, respectively. Each message M i is generated at every time and F i frames should be transmitted within the deadline of M i. The deadlines of periodic messages are assumed to be the end of their periods. We assume that demand priority network is a single segment with only one repeater and there is no promotion of normal priority frame to high priority. These assumptions will be removed in Section 4.4. The maximum frame transmission time, denoted by T fmax, is defined as sum of propagation delay of the maximum length of 82.3 frame(15 bytes) and inter-frame gap. 3.2 Limitations of demand priority protocol The prioritized round robin polling of demand priority network has two properties. First, network bandwidth is equally shared among active nodes at each priority level. Second, the worst case network access delay is bounded. Network access delay means the elapsed time between the transmission of two consecutive high priority frames at a node. When N nodes are connected to a repeater, the worst case network access delay of node i will be NT fmax,which is sum of transmission time of one normal priority frame and (N, 1) high priority frames at other nodes. The worst case response time of periodic messages is useful to determine whether their deadlines can be met. The response time of periodic message is defined to be the elapsed time from its arrival to completion of its transmission. Let R i denote the worst case response time of periodic message M i. The worst case situation which causes the longest response time of periodic message M i occurs when a normal priority frame is being transmitted and N periodic messages arrive simultaneously at all nodes and the repeater selects node (i mod N )+1, which first starts high priority frame transmission. This situation is similar to the critical instants[5]. R i can be calculated as follows: It takes NT fmax before the first frame of M i is transmitted. Once high priority frames are pending, there is no transmission of normal priority frames. Thus, the worst case network access delay after transmission of the first frame will be (N, 1)T fmax. The total network access delay of F i, 1 frames other than the first frame is (F i, 1)(N, 1)T fmax. Finally, the transmission of frames of M i takes F i T fmax. From the above discussion, we obtain the worst case response time R i. R i = NT fmax +(F i, 1)(N, 1)T fmax + F i T fmax = (F i N +1)T fmax (1) If R i is less than or equal to the deadline, periodic message M i always meets its deadline. The worst case response time given by Eq. (1) assumes that all nodes other than i continue to transmit their high priority frames until the transmission of M i is completed. However, this assumption is too pessimistic to calculate R i accurately. R i can be enhanced by considering the number of frames and periods of other periodic messages. Under the aforementioned situation, one normal priority frame delays the transmission of M i. The transmission of M i can be delayed by the frames of M j where i 6= j. Each time M j arrives, min(f i ;F j ) of

4 frames can be overlapped with M i. Because M j may arrive more than once before completion of M i, the total delay caused by M j cannot exceed d Ri emin(f i ;F j )T fmax. Thus, R i may be expressed as follows: R i = T fmax +F i T fmax + j6=i d R i emin(f i ;F j )T fmax (2) Note that R i appears on both sides. By rewriting Eq. (2), we obtain the following recurrence relation. Ri n = (F i +1)T fmax + d Rn,1 i emin(f i ;F j )T fmax P j6=i j where R i =;n 1 (3) According to [4, 13], if utilization of periodic messages is less than 1, the sequence Ri n converges in a finite number of steps. Let Ri be the value of Rn i when Ri n = Ri n,1.if the worst case response time Ri is less than or equal to, then periodic message M i always meets its deadline. This is a sufficient but not necessary condition, because we still overestimate the delay caused by other nodes. Most real-time messages should be handled with multiple priority levels required by application semantics or timing constraints. From Eqs. (1) and (3), it is obvious that demand priority MAC protocol causes the periodic messages at low priority level to block repeatedly the transmission of periodic messages at high priority level. When M i is the highest P priority message, the blocking time amounts to N T fmax + j6=i d R i emin(f i ;F j )T fmax. The blocking time may cause the violation of timing constraints. For example, we consider four periodic messages as shown in Table 1. We assume that these messages arrive simultaneously at time and node 1 begins the frame transmission. All frames have the same length and T fmax is about.12 ms. Figure 4 shows the sequences of frames transmitted. M 1 cannot meet its deadline, blocked by the transmission of other nodes. Message F i M ms M ms M ms M ms Table 1. A simple set of periodic messages M 1 M 2 M 3 M 4 Deadline miss (ms) Figure 4. Problem of round robin polling 4 Scheduling periodic messages In this section, we resolve the limitations of demand priority MAC protocol described in Section 3.2. We first describe how our message scheduling algorithm guarantees the deadline of periodic messages. Then schedulability conditions of periodic messages are analyzed. Proposed schedulability conditions will be shown to be sufficient and necessary. 4.1 Proposed scheduling algorithm Multiple priority levels are used to guarantee the deadline of periodic messages. The priority of periodic message M i is denoted by i and can be assigned by static or dynamic policy. To enforce the priority-based message transmission, two broadcasts are used to notify all nodes of priority and completion of periodic message, respectively. Thus, the communication demand of M i, denoted by C i, amounts to 2T bcast +F i T fmax where T bcast stands for the time taken to transmit a broadcast frame( 5 s). The details of our scheduling algorithm are described as follows. When a periodic message M i arrives, node i sends REQ H signal to the repeater. After node i is granted, it broadcasts message request frame comprised of M i and i. On receipt of message request frame, each node inserts it into the ready queue sorted in priority order. If M i is at the head of the ready queue, node i transmits the frames of M i using high priority frames. Otherwise, each node defers sending REQ H until its periodic message is at the head of ready queue or it has a new periodic message. Thus, only the frames of the highest priority periodic message continue to be transmitted. When a node completes the transmission of the periodic message, it broadcasts message completion frame. On receipt of message completion frame, each node deletes that message from the ready queue. If the ready queue is not empty, the next periodic message at the head of ready queue will be transmitted. Otherwise, normal priority frames are transmitted or network becomes idle. In summary, Figure 5 shows the pseudo-code of the scheduling algorithm, which node i executes at the device driver level.

5 ' $ M 1 Algorithm /* Running on node i, 1 j N */ Loop forever if (new periodic message Mi arrives) then Send REQ H to the repeater; f := ; if (node i is granted) then if (there is a periodic message) then if (f =) Broadcast message request frame (Mi;i); else if (f = Fi +1) Broadcast message completion frame; else Transmit the f-th frame; f := f +1; else if (there are normal priority messages) Send a normal priority frame; if (message request frame of Mj is received) Insert (Mj ;j) into ready queue in priority order; if (message completion frame of Mj is received) Delete Mj from ready queue; if (Mi is the head of ready queue) Send REQ H to the repeater; else if (ready queue is empty and normal priority messages are pending) Send REQ N to the repeater; & else Send to the repeater; end Loop Figure 5. Pseudo-code of scheduling algorithm Figure 6 shows how the messages in Table 1 are scheduled by our algorithm. The priorities of messages are static such that 1 > 2 > 3 > 4. As shown in Figure 6, all the messages meet their deadlines. From time, message request frames are transmitted in round robin order. Note that a periodic message is blocked only by message request frames and at most one data frame of lower priority periodic messages. Next, we analyze the schedulability of the proposed scheduling algorithm depending on message priority assignment policy. Static and dynamic priority assignment will be considered. 4.2 Static priority assignment When static priority assignment policy is used, every periodic message M i has a fixed priority value. We assume M 2 M 3 M (ms) broadcast frame data frame Figure 6. Priority-driven scheduling result of periodic messages given in Table 1 that priorities are assigned based on the rate monotonic method[5]. Without loss of generality, we assume that periodic messages are indexed in rate monotonic priority order such that P 1 P 2 ::: P N. The worst case response time of periodic message is used to determine whether the message can meet its deadline or not. Under rate monotonic priority assignment, Ri, the worst case response time of M i, can be obtained from the recurrence relation given by Eq. (4). Ri is defined as the value of Rn i when Rn i = Ri n,1. X R n i = T fmax +(N, i)t bcast + C i + i,1 (d Rn,1 i % Theorem 1 When the priorities of periodic messages are assigned by rate monotonic policy, each periodic message M i meets its deadline if and only if Ri, 1 i N. j=1 where R i ec j ) =;n 1 (4) Proof: The response time of periodic message M i depends not only on the communication demand of M i but also higher or lower priority periodic messages. The response time of M i can be delayed by the preemption of higher priority messages M 1 ;M 2 ;:::;M i,1. Moreover, the transmission of M i can be delayed by lower priority messages M i+1 ;:::;M N and a normal priority frame used for nonreal-time traffic. The time delayed by lower priority periodic messages and a normal priority frame is called blocking time B i where C i denotes the communication demand of M i. The worst case situation that maximizes M i s response time R i is as follows: While a normal priority frame is transmitted, N high priority messages arrive simultaneously. Then the repeater selects the node (i mod N )+1 which first starts transmission of high priority frame after the normal priority frame. B i equals the transmission time of one frame and (N, i) broadcast frames contributed by the periodic messages with lower priority than M i. B i = T fmax +(N, i)t bcast (5)

6 The preemption time of M i depends on the number of arrivals of higher priority messages during the response time R i. Since our algorithm allows only the highest priority message to be transmitted, the accurate preemption time can be calculated as in Eq. (6). Xi,1 j=1 (d R i ec j ) (6) From Eqs. (5) and (6), R i can be written in the following recurrence form. R i = B i + C i + Xi,1 j=1 (d R i ec j ) (7) Eq. (7) is equivalent to Eq. (4), so we can obtain R i. Thus, each message M i, 1 i N, always meets its deadline, if and only if the worst case response time R i Dynamic priority assignment When a dynamic priority strategy is used, the priority of messages varies with their arrival time. We analyze the schedulability of periodic messages based on EDF(earliest deadline first) policy. EDF policy is shown to be optimal in that if any dynamic priority assignment can produce a feasible schedule, EDF policy also produces a feasible schedule[5]. In real-time periodic task scheduling, EDF policy always guarantees the individual deadlines of periodic task instances if and only if utilization of periodic tasks is less than or equal to 1. However, this property cannot be applied to EDF-based periodic message scheduling in demand priority network. It is due to the effect of a normal priority frame. As described in Section 2, high priority frames cannot preempt a normal priority frame being transmitted. Thus the periodic messages can be blocked by at most one normal priority frame. Schedulability condition of periodic messages under EDF should include this blocking time. The total utilization of periodic messages U is the sum of utilization rates contributed by each message, i.e., U = i=1 C i (8) If U is less than 1, the transmission of normal priority frames is allowed. Thus, we define a new schedulability metric U : U = 8< : T fmax LCM(P 1;P 2;:::;P N ) + U if U<1 U if U =1 1 otherwise Theorem 2 When the priorities of periodic messages are assigned by EDF policy, all periodic messages meet their deadlines if and only if U 1. (9) Proof: First, we show the necessary condition. Periodic messages repeat the same arrival patterns at every LCM (P 1 ;P 2 ;:::;P N ) time. LCM (P 1 ;P 2 ;:::;P N ) is called a hyperperiod. Total communication demand of high priority messages over the hyperperiod is equal to P N LCM(P 1;P 2;:::;P N ) i=1 C i. For the messages to be schedulable, the total communication demand should be less than or equal to LCM (P 1 ;P 2 ;:::;P N ). N Case 1: i=1 LCM(P 1;P 2 ;:::;P N ) Ci = LCM (P1;P2;:::;PN). We divide both sides by LCM (P 1 ;P 2 ;:::;P N ). Then the above condition is rewritten as: i=1 C i =1 From Eq. P (8), U =1. By definition, U =1. N Case 2: i=1 LCM(P 1;P 2 ;:::;P N ) Ci <LCM(P1;P2;:::;PN ). The above condition implies U < 1. WhenU < 1, a normal priority frame may delay the transmission of high priority frames. While a normal priority frame is transmitted at the beginning of a hyperperiod, the transmission of high priority frames can be delayed by the transmission time of at most one frame. Thus, we consider the transmission time of one normal priority frame as blocking time. T fmax + i=1 LCM (P1;P2;:::;PN) Ci LCM (P1;P2;:::;PN) Pi By dividing both sides by LCM (P 1 ;P 2 ;:::;P N ), we obtain U 1. Thus, the necessary condition is proved. Now, the sufficient condition is proved. From Eq. (9), the condition of U 1 implies that U =1or U<1. Case 1: U =1 Because the utilization of periodic messages is 1, there is no transmission of a normal priority frame. From the proof found in [5], EDF policy produces a feasible schedule. The condition implies that U =1. Case 2: U<1 If there is no blocking caused by a normal priority frame and U<1, messages are schedulable by the proof found in [5]. In order to cancel the blocking time of a normal priority frame, there should be enough spare time over the hyperperiod: T fmax LCM (P 1 ;P 2 ;:::;P N )(1, U ). This can T be rewritten as U + fmax LCM(P 1;P 2;:::;P N ) 1. Thus, the messages are schedulable regardless of the blocking of a normal priority frame if U Extended schedulability analysis We will relax two assumptions described in Section 3.1. First, the assumption of a single-level network with one repeater is removed. When demand priority network consists of multiple repeaters, the maximum frame transmission time T fmax varies depending on the location of the

7 source and destination nodes. T bcast also increases in proportion to the number of levels of repeaters. Let Tfmax i be the time taken to transmit one frame from node i to the destination of M i. Thus, M i s communication demand C i should be changed to Ci = T bcast + F i Tfmax i.lett fmax denote the maximum of transmission time of one frame between nodes i and j where 1 i; j N. Since the normal frame transmission time is increased, T fmax in Eqs. (4) and (9) should be replaced by Tfmax. By replacing C i and T fmax with Ci and T fmax, Eqs. (4) and (9) are applied to determine the schedulability of periodic messages in demand priority network with multiple repeaters. Second, the promotion of normal priority frames is considered. Let T prom denote the promotion time of normal priority frame. The promotion of normal priority frame occurs when the busy period of high priority frames exceeds T prom. Under the static priority assignment, the promotion of normal priority frame should be added to the blocking time. The response time of M i isrevisedtobe Ri n = (b Rn,1 i c +1)T fmax +(N, i)t bcast + T prom C i + X i,1 (d Rn,1 i j=1 ec j ) where R i =;n 1 If Ri from the above equation is less than or equal to, then M i meets its deadline. When the dynamic priority assignment is used, BP max,the longest busy period of periodic messages within a hyperperiod, can be obtained as follows: Total communication P demand of periodic messages within [;t] amounts N to d t i=1 ec i.thevalueofbp max is determined at the earliest time(t min ) when the total communication demand becomes less than t. BPmax = i=1 d t min Pi eci where tmin = minftjp N i=1 d t eci <t;t2 Sg and S = f(k, 1)Pj jk =1; 2;:::; LCM (P 1;P2;:::;PN ) ; 1 j N g Pj If B max T prom, there are at most b BPmax T prom c cases of promotions; otherwise, no promotion. For periodic messages to be schedulable, the following inequality should be satisfied. BP max + b BP max T prom ct fmax t min 5 Performance evaluation schedulability conditions affected by priority assignment strategies. To compare the performance of the proposed algorithm with that of existing approach, we conduct a simulation study. The performance criterion is the guarantee ratio of periodic messages. A set of periodic messages is said to be guaranteed, only if all periodic messages in the set meet their deadlines. The ratio means a proportion of the number of message sets guaranteed by the scheduling algorithm to the total number of message sets used in the experiment. In simulations, we change the utilization of periodic messages and the number of nodes. Five different utilizations of periodic messages are chosen: 5%, 6%, 7%, 8%, and 9%. The number of nodes considered is 4, 8, 12, and 16. For each pair of f5%; 6%; 7%; 8%; 9%g f4; 8; 12; 16g, we generate ten thousand sets of periodic messages, whose length and period are assumed to have an exponential distribution. The experimental results in Figure 7 show that the proposed scheduling algorithm significantly improves the guarantee ratio compared with demand priority protocol. We also examine the overhead of the proposed scheduling algorithm. Our algorithm requires two broadcasts, although the length of broadcasted frame is much shorter than that of periodic message. According to the simulation, the ratio of the total time taken to broadcast over LCM (P 1 ;P 2 ;:::;P N ) to LCM (P 1 ;P 2 ;:::;P N ) is less than.7%. Thus, the broadcast overhead is negligible. Guarantee ratio Guarantee ratio DP Static Dynamic The number of nodes = Utilization of periodic messages(%) DP Static Dynamic The number of nodes = 8 From the previous discussion, we propose a prioritydriven message scheduling algorithm and analyze its Utilization of periodic messages(%)

8 Guarantee ratio Guarantee ratio Conclusion DP Static Dynamic The number of nodes = Utilization of periodic messages(%) DP Static Dynamic The number of nodes = Utilization of periodic messages(%) Figure 7. Experimental results This paper concentrates on the scheduling of periodic messages in the IEEE demand priority network. We have proposed a priority-driven preemptive message scheduling algorithm and analyzed the schedulability of periodic messages according to priority assignment policies. We showed sufficient and necessary conditions which determine the schedulability of periodic messages. The proposed scheduling algorithm can be implemented at the device driver level on top of demand priority MAC layer. Real-time systems have aperiodic messages as well as periodic messages. Aperiodic messages may have hard or soft deadlines. If a hard aperiodic message has a known minimum inter-arrival time, it can be transformed into the periodic message of which period equals its minimum interarrival time. Thus, our scheduling algorithm can be applied to the scheduling of hard aperiodic messages. The objective of soft aperiodic message scheduling is to minimize the response time. Since it is similar to the problem of aperiodic task scheduling, soft aperiodic messages can be handled effectively by applying the scheduling algorithms proposed in [1,2,1,11,12]. IEEE Committee is in the process of standardizing the burst mode, which allows the transmission of multiple frames per grant. The support of burst mode improves the efficiency of demand priority network at higher transmission speed. However, the burst mode can increase the worst case network access delay. The burst size of each node should be determined to bound the worst case access delay. When periodic messages are transmitted in burst mode, the appropriate burst size should be investigated to guarantee their deadlines. Consequently, one can take advantage of the results of schedulability analysis in this paper to determine the appropriate burst size. References [1] R. I. Davis, K. W. Tindell, and A. Burns. Scheduling slack time in fixed-priority pre-emptive systems. In Proceedings of the Real-Time Systems Symposium, pages , Dec [2] T. M. Ghazalie and T. P. Baker. Aperiodic servers in a deadline scheduling environment. Real-Time Systems, 9(1):31 67, [3] J. Grinham and M. Spratt. IEEE demand priority and multimedia. In Proceedings of the 4th International Workshop on Network and Operating Systems Support for Digital Audio and Video, pages 75 86, Nov [4] M. Joseph and P. Pandya. Finding response times in a realtime system. BCS Computer Journal, 29(5):39 395, [5] C. L. Liu and J. W. Layland. Scheduling algorithms for multiprogramming in a hard real-time environment. Journal of the ACM, 2(1):46 61, Jan [6] P. Martini and J. Ottensmeyer. Real-time communication in the demand-priority LAN: The effects on normal priority traffic. In Proceedings of 2th Conference on Local Computer Networks, pages , Oct [7] IEEE Standard Demand priority access method, physical layer and repeater specification for 1 Mb/s operation. IEEE, [8] M. Molle and G. Watson. 1Base-T/IEEE 82.12/Packet Switching. IEEE Communications Magazine, 34(8):64 73, [9] J. Ottensmeyer and P. Martini. Improving the demandpriority protocol. In Proceedings of the 4th International Conference on Computer Communications and Networks, pages , Sept [1] S. Ramos-Thuel and J. P. Lehoczky. On-line scheduling of hard deadline aperiodic task in fixed-priority systems. In Proceedings of the Real-Time Systems Symposium, pages , Dec [11] B. Sprunt, L. Sha, and J. P. Lehoczky. Aperiodic task scheduling for hard real-time systems. Real-Time Systems, 1:27 69, Dec [12] M. Spuri and G. C. Buttazzo. Efficient aperiodic service under earliest deadline scheduling. In Proceedings of the Real-Time Systems Symposium, pages 2 11, Dec [13] K. W. Tindell, A. Burns, and A. J. Wellings. An extendible approach for analyzing fixed priority hard real-time tasks. Real-Time Systems, 6(2): , [14] G. Watson, A. Albrecht, J. Curcio, D. Dove, S. Goody, J. Grinham, M. Spratt, and P. Thaler. The demand priority MAC protocol. IEEE Network, 9(1):28 34, 1995.