Analysis of WRR Queue Service Measurements
3.4 Determination of Available Capacity in a “Full” Virtual Path
3.4.3 Determination of Added Queue Size
The required maximum queue length, MQL, of the queues serving “normal” traffic streams accepted prior to the virtual path being “full” is determined as discussed in Sections 3.1 and 3.2 “Additional” traffic stream cell rates are determined through the procedures described in Section 3.4. The “additional” traffic is served whenever timeslots are available in the “normal” queue schedule, rather than being served on a regular basis, as is the case for the “normal” traffic streams. Thus, a queue serving an
“additional” traffic stream will have a buffer size greater than the MQL determined for the “normal” queues serving traffic streams having the same cell rate.
Over “long” periods, the empty timeslot probabilities resulting from the characteristics of the “normal’ traffic streams is sufficient to ensure the overall availability of virtual path timeslots needed to support the “additional” traffic cell rate, provided that cells exceeding the required CLR have not been lost due to the
“additional” traffic queue size being too small. Over “short” periods, however, there is some probability that the “additional” traffic may be served for a time at a rate less than that required to maintain the “additional” cell rate. Queues of “additional”
traffic streams must be at least MQL in length even when being served regularly on a schedule corresponding to the “additional” traffic rate. Since “additional” traffic is not served on a regular basis, the length of queues in “additional” traffic streams admitted using methods described in Section 3.4 must be greater than the MQL of traffic streams of the same cell rate served by a regularly scheduled WRR cycle.
An “added” queue is served only when there are empty timeslots in the WRR cycle, and thus there is some probability of the “added” queue being served later than required by its SCR. This probability contributes to the probability of queue overflow if the queue is sized only to handle the MBS of the “added” traffic stream, using Equation 3.5. The availability of empty timeslots during worst case periods (periods where no cells from the “additional” traffic stream are being served by the WRR for a significant time) is used in determining the queue size needed to support the
“additional” connection at the required QoS.
Traffic that is policed using the GCRA algorithm, as discussed in Chapter 1 and [TMS4], will comply with GCRA(T,0) and GCRA(TS, ) for peak cell rate, PCR, τS and sustainable cell rate, SCR, respectively. A worst case scenario occurs when a source exclusively transmits maximum size bursts of MBS at the maximum periodic rate allowed by the GCRA policing algorithm. When this occurs, WRR cell slots associated with that traffic stream are unavailable for the longest possible time, before becoming available for the remainder of the overall period. A periodic cell stream with period which transmits a burst of MBS cells at the peak rate, with inter burst spacing of T has PCR=1/T, sustainable cell rate SCR=1/T
TS
MBS⋅
1=MBS⋅(TS −T)+T S,
and is compliant with the GCRA for both PCR and SCR [TMS4]. The relationship for this transmission pattern is shown in Figure 3-3.
… Time MBS·T
Overall Period = MBS·TS
T1=MBS·(TS-T)+T
Maximum Burst
Figure 3-3: Worst Case Maximum Burst Relationships for GCRA Policed Traffic
In a WRR having M queues, the worst case for the overall WRR corresponds to all M traffic sources transmitting at the worst case cell rate described above, with the bursts exactly overlapping where all sources are transmitting at the same rate with identical MBS, as shown in Figure 3-4.
Time
… MBS·T
Overall Period = MBS·TS
T1=MBS·(TS-T)+T
… Queue 1
… Queue 2
Queue M
. . .
Figure 3-4: Worst Case Scenario for M Queues of GCRA Policed Traffic
The above worst case scenario results in each of N timeslots in a WRR cycle being occupied by “normal” traffic for MBS cycles, leaving no timeslots available to serve the “additional” traffic stream. Considering an N timeslot WRR to consist of N queue equivalents each having SCR of
N SCR R
SCR N M VP
i i
E =
∑
==1
1
and each queue equivalent having a MBS of
∑
== M
j
j
E MBS
MBS N
1
1
will result in a worst case scenario for the given traffic pattern.
The “additional” traffic stream will be served at a rate of N cells per WRR cycle during the inter-burst period, T1, and will not be served at all during the burst period,
MBSE·T. For an “additional” traffic stream having a cell rate of SCRA, the queue length needed in addition to the MQL of Equation 3.5 may be found as follows.
The number of “additional” traffic cells arriving during the overall period of the existing traffic using the worst case equivalents discussed above will be
SCR
The number of “additional” traffic stream cells not served during the burst period of the existing traffic is
PCR
Based on the desired CLR, the number of “additional” traffic stream cells which can be lost, while still maintaining the required QoS, is
A
where εis the bound on CLR, as discussed in section 3.4. The “additional” traffic stream buffer length, , must, in addition to the MQL, be sufficient to insure that no more than N
which may be rearranged as
−
⋅
⋅
′=
E E
A
E SCR PCR SCR
MBS
L 1 ε
(3.25)
The required total maximum queue length required for the “additional” traffic stream is therefore , with being the buffer component associated with the burstiness of the serving mechanism, and MQL being the buffer component associated with the burstiness of the “additional” traffic stream. The use of
“additional” traffic stream queue lengths of ensures that the required CLR, as bounded by
MQL L
L
MQ ′= ′+ L′
MQL′
ε, will not be exceeded.
3.4.4 Summary
Both the single and multiple empty timeslot methods described in the previous sections result in an estimate of an allowable SCR rate of traffic entering a queue served by a WRR, after the served path is considered “full” based on normal CAC methods. The only unknown parameter required to determine in each case, based on Equations (3.19) and (3.24) is the mean number of empty slots per cycle,
RˆASCR
µX. This mean may be estimated in real time by measurement of the number of empty timeslots being sent to the virtual path as the WRR cycles. The relationships between µX and are shown in Figure 3-5 for the single empty timeslot method, and in Figure 3-6 for the multiple empty timeslot method.
RˆASCR
0 0.2 0.4 0.6 0.8 1
Normalized Mean Empty Slots per Cycle Added
Figure 3-5: Added Connection Cell Rate, Single Empty Timeslot Method
0 0.2 0.4 0.6 0.8 1
Normalized Mean Empty Slots per Cycle Added
Figure 3-6: Added Connection Cell Rate, Multiple Empty Timeslot Method
Both methods will be conservative in allowing the admission of “additional”
traffic to a “full” path. The single empty timeslot method is the more conservative of the two approaches, allowing the admission of a smaller traffic stream for a given mean number of empty timeslots, but requires fewer computing resources than the multiple empty timeslot method. Admission of significant amounts of “additional”
traffic are possible with both methods, with “additional” traffic rates averaging from 3.5 to 11.5 percent of the virtual path rate for CLR’s of 10-10 to 10-3 for the multiple empty timeslot method. Average ranges from 2 to 6.75 percent of the virtual path rate are possible using the single empty timeslot method. When “additional” VBR connections are included in the virtual path, the server will still allow some amount of non-conforming or low-priority cells to be sent in virtual path cell slots. This is possible since at a given point in time there is some probability that the “additional”
traffic queue(s) will be empty, thus not requiring service, when only non-conforming or low priority cells are at the head of some “normal” queues. Because of the
methods used in determining RASCR , the multiple empty timeslot method will fill a virtual path more fully with conforming or high-priority cell traffic than the single empty timeslot method, in return for the additional computing complexity. Both methods require the use of larger buffers than required for “normal” traffic streams having the same cell rate. Thus, either method may be used depending on specific equipment design and network configuration tradeoffs.
The next step in developing a workable CAC will be to determine a method for estimating the actual mean number of empty timeslots based on measurements of observed empty timeslots during cycles of the WRR.