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
T
Interarrival times of tasks
S
Service times of tasks (a vector of length n, or a matrix nrows=n, ncols='m').
N
Number of cores each task needs
m
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.
# 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# }