Wld: Workload of a High Performance Cluster model

Description

This function computes the Kiefer-Wolfowitz modified vector for a HPC model. This vector contains the work left on each of 'm' servers of a cluster for the time of the arival of a task. Two methods are available, one for the case of concurrent server release (all the servers end a single task simultaneously), other for independent release (service times on each server are independent).

Usage

Wld(T, S, N, m, method = "concurrent")

Arguments

Interarrival times of tasks

Service times of tasks (a vector of length n, or a matrix nrows=n, ncols='m').

Number of cores each task needs

Number of cores/servers for a HPC

method

Independent or concurrent

Value

A dataset is returned, containing 'delay' as a vector of delays exhibited by each task, 'total_cores' as the total busy CPUs in time of arrival of each task, and 'workload' as total work left at each CPU.

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

Run this code

# NOT RUN {
Wld(T=rexp(1000,1), S=rexp(1000,1), round(runif(1000,1,10)), 10)
# returns the workload, delay and total cpus used 
# for a cluster with 10 CPUs and random exponential times
# }