Information Technology Reference
In-Depth Information
M/M/1 queuing systems assume a Poisson arrival process. This is a very good ap-
proximation for the arrival process in real systems that meet the following rules:
1. The number of customers in the system is very large.
2. The impact of a single customer on the performance of the system is very small.
3. All customers are independent.
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In the M/M/1 model, the probability of exceeding a particular number of cus-
tomers in the system decreases geometrically, and if interrupt requests are considered
customers, then the two such requests in the system have a far greater probability
than three or more such requests (LaPlante, 2002). This means that a system that can
tolerate a single time overload should be able to contribute to the system's reliability.
Another type of queuing model is the M/M/c model. This type of model is a
multiserver model. Another useful queuing theory is Erlang's formula. If there are m
servers, then each newly arriving interrupt is serviced by a process, unless all servers
are busy. In this instance, the customer or interrupt is lost. The Erlang distribution can
be used to model service times with a low coefficient of variation (less than one), but
it also can develop naturally. For instance, if a job has to pass, stage by stage, through
a series of r independent production stages, where each stage takes a exponentially
distributed time, then the analysis of the M
=
Er
=
1 queue is similar to that of the
M
=
M
=
1 queue (Adan & Resing, 2002).
17.4
PERFORMANCE ANALYSIS
Performance analysis is the study of a system, especially a real-time system, to see if
it will meet its deadlines. The first step in performing this type of analysis involves
determining the execution of code units. The ability to calculate the execution time
for a specific real-time system can be critical because the system's parameters, such
as CPU utilization requirements, are calculated beforehand. With this information,
the hardware and the software of a system is selected as well. There are several
methods available to conduct performance analysis.
One way to measure real-time performance estimate is though an execution time
estimate in which the execution time is calculated by the following:
execution time
instruction timing
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The path is the sequence of instructions executed by the program, and the instruc-
tion timing is determined based on the sequence of instructions traced by the program
path, which takes into account data dependencies, pipeline behavior, and caching.
The execution path of a program can be traced through a high-level language specifi-
cation; however, it may be difficult to obtain accurate estimates of total execution time
from a high-level language program, as there is not a direct correspondence between
=
program path
+
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http://www.eventhelix.com/realtimemantra/CongestionControl/m m 1 queue.htm
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http://www.embedded.com/design/multicore/201802850
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