StabC: Stability constant for a workload of a High Performance Cluster model
Description
This function calculates the constant C that is used in the stability relation
of a model, which is basically the following: lambda/mu<C, where lambda
is the intensity of task arrivals, and mu is the intensity of service,
in this case it is 1/(mean service time). The constant depends only on
the number of cores in the model and the distribution of core requirement
of tasks. Note that there are three methods of calculation: two of them
calculate the exact value ("less-memory" and "more-memory"), and the third
one ("monte-carlo") returns the approximate value. The exact value may
be calculated up to a number of cores of the order of 100. The constant
is valid only for the model with simultaneous task service by cores.
the distribution of number of cores required by a task, a vector with values for probability of a task requiring 1..s cores
maxiter
number of iterations for Monte-Carlo method
method
monte-carlo, less-memory, more-memory (approximately 1.5 times faster, but needs more memory)
Value
The value of a constant C in the relation lambda/mu < C is returned
References
E.V. Morozov, A.Rumyantsev. Stability analysis of a multiprocessor model describing
a high performance cluster. XXIX International Seminar on Stability Problems for Stochastic
Models and V International Workshop "Applied Problems in Theory of Probabilities and
Mathematical Statistics related to modeling of information systems". Book of Abstracts. 2011. Pp. 82--83.
# NOT RUN {StabC(s=2,p=c(.5,.5), method="less-memory")
# returns the constant for a 2-server model, # where a task needs 1 or 2 cores with equal probability# }