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Applied Mathematics |Прикладная математика

LESSON 8

Read the text: SPACE VEHICLE BUFFER ANALYSIS

Using engineering estimates for Space Vehicle (SV) processing times, potential bottlenecks within the SV were identified. A significant concern was that of the output buffers onboard the SV for K-Band Gateway and K-Band Crosslink traffic being insufficiently sized. A modeling proposal with assumptions about SV performance was formulated and presented to the customer for approval. The C++ prototype that was developed within a month was used to carry out a detailed study of possible buffer overflow conditions and the effects of queuing. It was determined that the arrival process for packets was much more orderly than theory would have predicted and that much less queuing could be expected. The probability of buffer overflow was determined to be essentially a function of utilization and was much lower than expected. The buffers were appropriately sized. Results were presented to the customer and were well-received.

Space Vehicle CPU Burst Analysis

This on-going engineering analysis examines the processing of calls by the Central Processing Unit (CPU) onboard the SV as its footprint passes over a "hot" spot on earth, e.g. Tokyo at a particularly busy time. In particular, a C++ discrete event simulation model was developed in two months and used to determine the average delay for call completions and the number of blocked or dropped calls as functions of simulation time for various parameter sets. An initial burst of call activity assumed a peak rate for call handoffs, setups, and teardowns with call activity settling down to an off-peak rate. The off-peak rate was maximized to determine a rate of service for the system subject to the constraint that blocked or dropped calls be maintained at a given percentage of total calls. Each parameter set was defined by the maximum number of calls the SV could process, the fraction of the peak rate assumed for the off-peak rate, and the duration of the initial burst period.

Results showed that average delay increased with longer burst durations regardless of queue size. An increased number of blocked or dropped calls resulted from longer burst durations in general, but was reduced during the burst period with a larger queue size. Fewer calls were blocked during a given burst period with the larger queue size, but the average delay (across all call types) was greater when the off-peak rates were maximized. Holding the percentage of blocked calls to a given percentage meant that the complementary percentage of total calls were completed for a given maximum off-peak rate. The same approximate maximum for the off-peak fraction regardless of burst duration or queue size (maximum number of calls) was determined to be the rate of service for the system given the CPU times for handoff, setup, and teardown.

1. Match the left part with the right:

2. Complete the sentences with the suggested words: predicted, expected, overflow,  process

       It was determined that the arrival _____________for packets was much more orderly than theory would have _____________and that much less queueing could be expected. The probability of buffer _____________was determined to be essentially a function of utilization and was much lower than_____________.