hpcwld (version 0.5)

ApproxC: Approximate, dynamic iterative computation of the 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 this method of calculation allows to stop on some depth of dynamics, thus allowing to calculate an approximate value in faster time. The constant is valid only for the model with simultaneous task service by cores.

Usage

ApproxC(s, p, depth=3)

Arguments

s

number of cores/servers for a HPC

p

the distribution of number of cores required by a task, a vector with values for probability of a task requiring 1..s cores

depth

the depth of dynamical calculation. By default calculates up to groups of 3 tasks occupying the CPUs. When depth=s, calculates the exact value. However, depth=s might take a bit more time.

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.

Examples

# NOT RUN {
StabC(s=2,p=c(.5,.5))
# returns the constant for a 2-server model, 
# where a task needs 1 or 2 cores with equal probability
# }