Deterministic protocols for real-time communication in multiple ...

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S. Norden et al. / Computer Communications 22 (1999) 128–136 131Table 1Node and channel status table (MDCR)Time N 1 N 2 N 3 N 40 (5, 17) (2, 6) (2, 9) (2, 12)1 C C C C2 N (5, 17)3 X (5, 17)4 X (5, 17) D (2, 6)5 X (5, 17)7 X (5, 17) D (2, 9)8 I I9 N (2, 12)10 X (2, 12)11respect to its predecessor, and modifying the laxity of itssuccessor. Messages with negative laxity are removed fromthe queue.The LDCR protocol consists of three phases, namely,contention mode, collision resolution (CR) mode, andleast laxity first (LLF) mode, which are described below.This combination of CR mode and LLF mode defines anepoch in the LDCR protocol as contrasted to the DCR preorder and MDCR protocols wherein an epoch is the CRmode alone.1. Contention mode (when channel is idle)(a) Each node examines the message at the head of itsqueue. If the laxity of the message is negative, themessage is dropped.(b) Otherwise, it attempts to transmit notifier for themessage.(c) If the notifier transmission is successful, themessage is transmitted.(d) If a collision occur during notifier transmission, allnodes enter into CR mode by traversing the CR tree inpre order.Table 2Node and channel status table (LDCR). C: Collision; N: Notifier; X: Transmit;D: Drop; L: Laxity; I: IdleTime N 1 N 2 N 3 N 40 (5, 17) (2, 6) (2, 9) (2, 12)1 C C C C2 N (5, 17)3 Defer (L 1 ˆ 9) C C4 (L 1 ˆ 8) N (2, 6)5 (L 1 ˆ 7) X (2, 6)7 (L 1 ˆ 5) N (2, 9)8 X (2, 9)10 (L 1 ˆ 2) N (2, 12)11 X (2, 12)12 LLF mode – (L 1 ˆ 0): X (5, 17)172. Collision resolution mode(a) When a node n i gets its turn in the CR mode, ittransmits its notifier. Thus every other node is informedof the message requirements of node n i(b) If the laxity of a message (first message at queue ofn i ) is less than a threshold (but non-negative), then themessage is transmitted, else the message is deferred andper order traversal continues. It two or more messageshave the laxity less than or equal to the threshold value,the preference is given to message with shorter servicetime. This minimizes the time that the channel isblocked, thereby improving the chances of successfultransmission for subsequent messages.(c) Even after the CR tree is completely traversed, ifsome deferred messages are still to be transmitted, theprotocol enters into the LLF mode.3. LLF mode(a) In the LLF mode, all the deferred messages aretransmitted, based on the least laxity order of messagesamong nodes. This phase is required to enable thosemessages, that arrived in the current epoch, to be transmittedbefore the next epoch. By doing this, the overheadincurred as result of collision between messages oftwo different epochs is eliminated.(b) If all the messages are either transmitted or dropped,the next epoch begins.Note that the threshold value mentioned in Step 2(b) isfixed, in our protocol, to be one. The importance of thisvalue, is brought out in a subsequent section, when comparingthis protocol with another representative protocol.3.4.2. Illustrative examplesIn this section, we demonstrate the effectiveness of theLDCR over MDCR with an illustrative example. The exampleconsiders a LAN with 4 nodes. Tables 1 and 2 depict theworking of MDCR and LDCR, respectively. The first entry(at time 0) in these tables is the initial status of the queue ateach node (each node has a single message to transmit). Forexample, node N 1 has a message having deadline of 17 andrequiring 5 slots for transmission. In this example, the preorder traversal of CR tree (binary tree), as shown in Fig. 1, isin the order of N 1 ,N 2, N 3, and N 4.Let us trace a few steps in the MDCR protocol shown inTable 1. At time 1, all nodes attempt to transmit their notifierwhich results in collision, thus all nodes enter the CRmode. At time 2, N 1 (root of the CR tree) transmits itsnotifier, and proceeds to transmit its message from timeslot 3 onwards, for 5 time slots. Thus all nodes back offfor a period of 5 slots. Even though the laxity of thismessage is very large (10), compared to the laxity of othermessages, it is still transmitted. As result, the other nodes allend up having negative laxity, when they get their turn. Bytime 8, two nodes in the left subtree (N 2 and N 3 ) would droptheir messages, as their laxities become negative at the end
132S. Norden et al. / Computer Communications 22 (1999) 128–136Fig. 1. Mapping of nodes into vertices of CR tree.of slot 4 and 7, respectively. At time 9, the node in the rightsubtree (N 4 ) will transmit its notifier successfully, and transmitsits message successfully before the deadline.For the LDCR protocol, the threshold used for defermentis taken to be 1. The behaviour of LDCR protocol is similarto MDCR up to time 2, i.e., after transmission of the notifierof message at N 1 . After transmission of the notifier, theLDCR computes the laxity for this message and finds thatthe laxity is greater than threshold, hence defers themessage. At time slot 4, N 2 transmits its notifier, and findsthat the laxity of the message is zero, hence the message istransmitted immediately. The protocol proceeds in thismanner.From the above example, it can be noted that the LDCRprotocol transmits all the messages successfully, while theMDCR protocol can transmit only 50% of the messages.The key aspect that contributes to the improved performancein LDCR is the deferment of the message at N 1 ,which has a large laxity. This allows more critical messagesat N 2 , N 3 , etc., to be transmitted before their deadlines.4. Simulation studiesTo study the effectiveness of the proposed protocols, wehave conducted extensive simulation studies. For eachsimulation run, 10000 messages were generated for theentire system. For the performance results, 95% confidenceintervals were obtained. The performance metrics used, andthe simulation model are defined below:4.1. Simulation model and parameters• N: Number of nodes on the network.Table 3Simulation parametersParameter Explanation Value when varied (fixed)N Number of nodes 5…30 (10)M Average message length 7…20 (20) slotsa Laxity parameter 2…25 (10)Load l M N 0.1…1 (0.6)P/Nt Packet to Notifier ratio 2…10 (10)• M: Average message length (or service time).• a: Laxity parameter which decides the deadline ofmessages, directly proportional to deadline. The deadlineis uniformly chosen in the interval [C i ,a*C i ].• l: Mean message arrival rate at a node. Message arrivalat each node follows Poisson distribution with mean arrivalrate l.• L: Load on the network is defined as the product ofnumber of nodes (N), mean message length (M), andthe arrival rate, i.e., L ˆ (l * M * N).• (P/Nt): Packet to notifier ratio. As mentioned earlier, slotis a basic unit of transmission in which one packet can betransmitted. We fix a normalized value of packet slot tobe 10 time slots, and from this ratio, we can determinethe number of slots used by transmission of a notifier,relative to this normalized value of a packet slot.The simulation parameters and their ranges are given inTable 3.4.2. Performance metrics• Success Ratio (SR): This is defined as the ratio of thetotal number of messages transmitted successfully to thetotal number of messages that arrived in the system. TheSR is an important metric which reflects the throughputof the network.• Effective Channel Utilization (ECU): This is the ratio ofthe time slots used for successful transmission to thenumber of time slots that elapsed until all messageswere transmitted or dropped. A higher value of ECUwould imply that the channel utilization, as result ofsuccessful message transmission, is large compared tothe net overhead as result of collision and notifier transmission.• Normalized Transmission Length (NTL): This is theratio of the mean length of the transmitted messages tothe mean length of the generated messages. The closer itsvalue to one, the less bias towards longer or shortermessages. In other words, when the NTL offered by aprotocol is one, the protocol behaves independent ofmessage service time.4.3. Results and discussionIn this section, we compare the performance of theproposed protocols (MDCR and LDCR) with a recentlyproposed protocol called PBCSMA. The PBCSMA protocolis chosen for comparison because it can support multipacketmessages, and has been reported to perform better than theVTCSMA and CSMA based protocols [15]. It is a modifiedversion of p-persistent CSMA with support for differentpriority levels of traffic. Note that the MDCR, LDCR, andPBCSMA are best effort protocols, which means that theyadmit all the messages arriving in the system, withoutguaranteeing that these messages will be transmitted
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