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S. Norden et al. / Computer Communications 22 (1999) 128–136 133Fig. 2. Effect of load on (a) SR,(b) ECU,(c) NTL.successfully. In the simulation plots, these protocols arelabelled as with an extension BE to indicate ‘‘Best Effort’’.For the sake of completeness, we describe the PBCSMAprotocol as given below:The PBCSMA protocol• A message is characterized as critical, if its laxity is lessthan a predefined threshold, otherwise it is classified asnon-critical.• Transmission of a critical message begins with the broadcastof a notifier, similar to our protocol.• When a new message arrives and is classified as eithercritical or non-critical, and the channel is idle, themessage is sent. Otherwise (i.e., the channel is busy),if the message currently being transmitted is not critical,it is preempted to allow a critical message to besent.• Transmission of a non-critical message from a node isnot possible as long as the channel is busy. Also, themessage is not sent right after the channel becomesidle. The node waits for one slot, and if the channelremains idle, the message is sent.• Following a collision, a non-critical message issuspended for the duration of a slot, and if that slot isnot occupied by a critical message, the non-criticalmessage is retransmitted with probability P i .• If a critical message collides, it is retransmitted immediatelywith probability P i .From the Figs. 2(a)–5(a), it can be observed that the SRoffered by LDCR is better than the other two protocols ofwhich the MDCR is better than PBCSMA. From Figs. 3(b)–5(b), the ECU obtained using LDCR is higher (better) thanthe other two because of its SR. Similarly, the NTL offeredby LDCR is closer to one as compared to the other protocols.The reasons for these observations are discussedbelow:• LDCR is better than PBCSMA: The reasons, why LDCRis an improvement over PBCSMA, are as follows. In thecase of the notifier of a critical message colliding with thenotifier transmission of another critical message,PBCSMA will retransmit the interrupted message withcertain probability. When the threshold is large, onecould have several critical messages which require tobe transmitted. Repeated attempts at retransmission withoutproper arbitration in the CSMA fashion will lead toseveral collisions utilizing several slots which in turnleads to missing of message deadlines. Whereas inLDCR-BE, by forcing the threshold for critical messagesto be one, the protocol restricts the number of criticalmessages; in the event of collision, the arbitration isdone as per the pre order traversal of the CR treeFig. 3. Effect of a on (a) SR, (b) ECU, (c) NTL.
134S. Norden et al. / Computer Communications 22 (1999) 128–136Fig. 4. Effect of N on (a) SR,(b) ECU,(c) NTL.allowing one of the nodes to transmit in subsequent slotswithout wasting the bandwidth. Further, in LDCR, whentwo critical messages have laxities less than the thresholdvalue, the smaller message is transmitted whichimproves the chances of subsequent messages. AsPBCSMA is a preemption based protocol, if a non-criticalmessage is preempted as result of the presence ofseveral critical messages, the assumption made in [15]is that the non-critical message will have a large enoughdeadline so as to still be transmitted after all the criticalmessages. This will not hold especially when the thresholdis large and there are a large number of criticalmessages waiting for channel access. The subsequentdelay incurred by the non-critical message may make itcritical, leading to degradation in the protocol as thenumber of critical messages steadily increases. Anotherinteresting observation about PBCSMA that reinforcesthe above point, also made by the author in [15], is thatthe SR will degrade when the threshold is increasedbeyond a certain value, as the number of criticalmessages (with varying degree of criticality) increases.This results in increased number of collisions betweenthese messages, thereby reducing the SR. The increasednumber of collisions will also result in a lower ECUvalue. In addition, it may also result in priority inversion,as high laxity (non-critical) messages would contend forthe channel along with low laxity (critical) messages.The increased number of collisions will also resultin a lower ECU value. This situation will not arisein LDCR, as it defers the non-critical messages to aseparate mode (LLF), thus avoiding collisions betweenmessages with high and low laxities. This will reducethe number of overall collisions. These deferredmessages are transmitted in the LLF mode, usinglaxity based ordering. This systematic way of collisionresolution and message deferment results in improvedSR and ECU. The superiority of the LDCR protocolover PBCSMA, can be clearly seen, from all the simulationgraphs.• LDCR is better than MDCR: The relatively poor performanceof MDCR is owing to its blind transmission ofmessages as per the static position of nodes in the CR treewithout taking into account the laxity of messages amongthe nodes. Thus higher priority (lower laxity) messageswill be treated in the same way as lower priority (largelaxity) messages. This will lead to missing of messagedeadlines. Further, a large number of messages with tighterlaxity, having small service times, could be dropped ifa message with larger laxity, and having larger servicetime, is transmitted. This scenario is brought out by thehigh NTL values, shown by the MDCR protocol, in Figs.2(c)–5(c). From the Figs. 2(a)–5(a), which study theFig. 5. Effect of P/Nt ratio on (a) SR,(b) ECU,(c) NTL.
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