Interference within the FTT-SE periodic model

The previous section generically described the interference phenomenon that occurs with several trac sources in a switched Ethernet network. To ad- dress this interference within the FTT-SE, the analysis has to conform with the periodic activation model, address the simultaneous scheduling of mul- tiple inter-dependent links and t additional constraints of the architecture, namely the additional inserted idle time (IIT) that results of strictly enforc- ing the synchronous window duration. The periodic scheduling model in FTT-SE considers Nsmessage streams (mi) which descriptors are stored in

the Synchronous Requirements Database Γ (Equation 3.1).

The streams are mainly characterized by the periodic activation release (Ti), message size (Ci) that can extend over several Ethernet packets and

the forwarding directions that include the sending link (Si) and one or more

receivers (R1 i..Rkii

 ).

4.3.1 Window connement

The FTT-SE scheduler strictly connes the periodic trac to the synchronous window, with maximum size of LSW . This means that when a message can- not be fully transmitted within this window, it is kept in the ready queue and the scheduling is suspended and resumed in next EC, as illustrated in

1 time 2 4 7 Xn EC_n Periodic window S 1 3 8 8 EC_n+1

Figure 4.3: Impact of inserted idle time.

Figure 4.3. This property prevents the window overrun but it introduces idle time that must be accounted for in the analysis.

The eect of such inserted idle time has been thoroughly studied in [27] for xed-priorities scheduling and [28] for EDF. Therein, it was shown that when scheduling within a periodic partition of length S and period E, as long as the message transmission time Ci is inated with a compensation factor,

becoming C0

i, as in Equation 4.1, with X being the maximum inserted idle

time upper-bounded by the maximum packet length. Any schedulability analysis for preemptive scheduling with xed or dynamic priorities applies.

C_i0 = Ci

E

S − X (4.1)

When considering utilization-based tests, the compensation factor can be applied to reduce the utilization least upper bound while the transmission times Ci are kept unchanged as shown in Equation 4.2. We will use this

approach in the remainder of this chapter. XC_i

Ti

≤ Ulub_×S − X

E (4.2)

4.3.2 Deferred release in the downlinks

The interference between messages referred to in Section 4.2 also aects the FTT-SE periodic trac. Such interference is responsible for the appearance of deferred release with jitter (Ji) in the downlinks. In fact, while in the

uplinks, i.e., in the nodes, the periodic activation pattern can be enforced easily by the trac scheduler, the same is not true in the downlinks. The amount of time that a message can be deferred in a downlink is directly related to the interference that it can suer in the respective uplink from the messages that are sent to dierent destinations (Figures 4.3 and 4.2). This interference may vary from instance to instance, leading to a jittered arrival of the message at the downlink.

The deferred release phenomenon also occurs at intra-EC scale, as shown in Figure 3.7 and discussed in Section 3.3.2, when building each EC-schedule. However, here we do not account for any intra-EC aspects and we deal solely with the trac scheduling at an EC scale and thus the deferred release jitter we are now concern with also occurs at this scale.

4.3.3 Scheduling multiple links

The scheduler operates over the message requirements data-base (SRDB) and builds a single global ready queue, serializing messages according to their priority, either static or dynamic. However, when dispatching the messages in the global ready queue, the protocol attempts to ll up the uplinks and downlinks in each EC in order to exploit as much as possible the parallel forwarding paths available in the switch.

This scheduling methodology approximates the model to a link oriented scheduling. The global ready queue is parsed in several ready queues, one per link, with the messages that traverse that link, and a scheduler that operates quasi-independently on each link with the restriction of scheduling messages together (in the same EC) in the uplinks and the downlinks. The intra-EC scheduling is handled according to the rules in Equation 3.2 that enforce the window protection and the causality eect between the uplink and the downlink.

Therefore, the trac on a specic downlink is in fact constrained by the trac explicitly submitted to that port and also the trac scheduled in the uplinks of each message, causing interference. In a multicast or broadcast transmission scenario, messages are only scheduled if tting the uplink and all downlinks in a given EC. In this case, it is enough to have one downlink full to prevent that message from being transmitted in that EC even if the other downlinks and uplink are lightly loaded. This represents a very strong interference. In a unicast message scenario this type of interference does not apply, since only one uplink and one downlink are involved. The interference veried in the uplink does not propagate to other downlinks.

In terms of schedulability analysis of a downlink, in the unicast scenario, only the interference from the uplinks is considered. However, in a multicast or broadcast messaging scenario, a multitude of interfering sources aecting the downlink must be considered. The interference in the downlinks is not conned to the trac in the uplinks but also to the trac in other down- links, which by themselves may suer interference from other uplinks and downlinks in a cascade procedure, pushing the complexity of the analysis to a higher magnitude.

Therefore, in this work we focus in the unicast scenario, only. At the end of this chapter a few considerations are done addressing the multi- cast/broadcast scenario.