ISSN:
1572-9125
Keywords:
05A15
;
05C05
;
68C15
;
68E10
;
real-time behaviour
;
FCFS scheduling
;
trees
;
probability
;
generating functions
;
singularity analysis
;
asymptotics
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We investigate some real-time behaviour of a (discrete time) single server system with FCFS (first come first serve) task scheduling under rush-hour conditions. The main result deals with the probability distribution of a random variable SRD(T), which describes the time the system operates without violating a fixed task service time deadlineT. Relying on a simple general probability model, asymptotic formulas concerning the mean and the variance of SRD(T) are determined; for instance, if the average arrival rate is larger than the departure rate, the expectation of SRD(T) is proved to fulfilE[SRD(T)]=c 1+O(T −3) forT→∞, wherec 1 denotes some constant. If the arrival rate equals the departure rate, we findE[SRD(T)]∼c 2 T i for somei≥2.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02074875
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