**Recent Queuing Simulations of the L2STTpp**

S.L. Linn -- Florida State

10 Apr 02

Abstract

Recent timing measurements of TFC I/O and processing times were
incorporated into the STT queuing simulation. Latencies of up to 250μs
were found with no dead time incurred for luminosity conditions four
times higher than expected in run 2b.

![](media/image1.jpeg){width="5.998611111111111in"
height="3.5097222222222224in"}

Figure 1. Schematic of the STT queuing simulation showing the six
independent sectors.

![](media/image2.jpeg){width="5.992361111111111in"
height="2.4923611111111112in"}

Figure 2. Schematic of one sector of the STT queuing simulation.

**1. Queuing Model**

The STT is modeled as six independent sectors as shown in Fig.1. Each
sector is modeled as a chain of processors with variable delays and
buffers (queues) as shown in the Fig.2.

Each sector randomly selects the number of tracks/sector and the number
of clusters/STC channel. The track distribution shown in Fig.3 is given
by a double exponential and the clusters distribution is given by a
double Gaussian. Events are generated with a Poisson distribution with a
mean time between events of 100μs and a minimum time between events of
9μs. Dead time inefficiency is computed as the ratio of input to output
events. Events can also be lost when buffer limits are exceeded or
processing time exceeds 500μs.

![](media/image3.jpeg){width="5.997222222222222in"
height="2.540277777777778in"}![](media/image4.jpeg){width="5.997222222222222in"
height="2.997916666666667in"}

Figure 3. Top-Clusters distribution modeled as a double Gaussian
distribution. Bottom-Track distribution modeled as a hyper-exponential
distribution (mean=1).

# 2. TFC Model

Due to limitations of the queuing simulation, it is not possible to
model individual tracks within the context of the full STT simulation,
which uses the number of tracks and clusters as attributes of an event.
For this reason a separate simulation of the TFC was done to determine a
parametric function to describe the TFC delay as a function of the
number of clusters and tracks. The part of the TFC between the input and
output DPM's buffers was simulated separately, so that individual track
processing times could be measured. Two quasi-independent banks of four
DSP's were modeled to include XBUS transfer times and processing.
Processing times were taken from recent measurements ( Hobbs and
Pancake, 4 Apr 02). Odd and even numbered tracks were processed by
separate DSP banks respectively.

To simplify the calculation the number of fits (NF) was assumed to be
1.5 resulting in a processing time for a single road (t2) given by

t2 (μs)=23.13 + 0.58 NHR,

If NHR=10, the following function can be used to describe the processing
as a function of the number of tracks (NR),

t(μs)= 27.7 (m+1) + 0.6 (8m-NR), where m=int\[(NR-1)/8\].

The resulting distribution is a step-like function which was
approximated by a step function with processing times of : 26μs
(NR=1-8), 54μs (NR=9-16), 81μs (NR=17-24), and 109μs (NR=25-32).
Smearing of the processing times due to a variable NHR and NF was also
studied; however, the variation was found to be less significant than
variations due to NR. The function used is shown in Fig 4.

For the full simulation of the STT, the simple step parameterization was
used with I/O times per road (t1,t2) of

t1(μs) = 3.31 + 0.03 NHR (event buffer to IDPM) ,

t3(μs) = 1.70 + 0.06 NHR (ODPM to Hotlink buffer).

**3. Results**

For the processing times associated with clustering finding and road
processing, the default timing estimates were used. Total processing
latency was measured for an average number of tracks/sextant of 1,2, and
4. In all but the last case, the dead time was zero, and buffers were
always less than four events deep. In the last case of four
tracks/sextant, a 0.1% dead time was measured, but this is very
sensitive to the exact shape of the input distribution, which was always
truncated at 32 tracks. The latency distribution for \<NR \>=4 is shown
in Fig.5 where maximum latencies of about 250μs are rarely exceeded. The
four peaks correspond to events with less than 8, 16, 24, and 32 tracks,
and the tails and fill-in correspond to events that were buffered while
waiting for ![](media/image5.wmf)processing.

Figure 4. Processing time vs. Number of Roads

![](media/image6.jpeg){width="5.996527777777778in"
height="4.250694444444444in"}

Figure 5. Events vs. total processing time(μs) .