scholarly journals Analysis of a 2-state discrete-time queue with stochastic state-period lengths and state-dependent server availability and arrivals

2019 ◽  
Vol 135 ◽  
pp. 102026 ◽  
Author(s):  
Freek Verdonck ◽  
Herwig Bruneel ◽  
Sabine Wittevrongel
Keyword(s):  
Discrete Time ◽  
State Dependent ◽  
Discrete Time Queue

Analysis of state-dependent discrete-time queue with system disaster

2019 ◽  
Vol 53 (5) ◽  
pp. 1915-1927
Author(s):  
Ramupillai Sudhesh ◽  
Arumugam Vaithiyanathan
Keyword(s):  
Discrete Time ◽  
Busy Period ◽  
System Size ◽  
Time Dependent ◽  
System Effect ◽  
Period Distribution ◽  
State Dependent ◽  
Discrete Time Queue ◽  
Formal Power ◽  
Time Dependent System

An explicit expression for time-dependent system size probabilities is obtained for the general state-dependent discrete-time queue with system disaster. Using generating function for the nth state transient probabilities, the underlying difference equation of system size probabilities are transformed into three-term recurrence relation which is then expressed as a continued fraction. The continued fractions are converted into formal power series which yield the time-dependent system size probabilities in closed form. Further, the busy period distribution is obtained for the considered model. As a special case, the system size probabilities and busy period distribution of Geo/Geo/1 queue are deduced. Finally, numerical illustrations are presented to visualize the system effect for various values of the parameters.

Model-Based Discrete Linear State Estimator for Nonlinearizable Systems With State-Dependent Noise

1990 ◽  
Vol 112 (4) ◽  
pp. 774-781 ◽  
Author(s):  
R. J. Chang
Keyword(s):  
Discrete Time ◽  
Continuous Model ◽  
Equivalent Model ◽  
State Estimator ◽  
Time Model ◽  
State Dependent ◽  
Present Technique ◽  
Linear State ◽  
Noisy Measurement ◽  
Time Linear

A practical technique to derive a discrete-time linear state estimator for estimating the states of a nonlinearizable stochastic system involving both state-dependent and external noises through a linear noisy measurement system is presented. The present technique for synthesizing a discrete-time linear state estimator is first to construct an equivalent reference linear model for the nonlinearizable system such that the equivalent model will provide the same stationary covariance response as that of the nonlinear system. From the linear continuous model, a discrete-time state estimator can be directly derived from the corresponding discrete-time model. The synthesizing technique and filtering performance are illustrated and simulated by selecting linear, linearizable, and nonlinearizable systems with state-dependent noise.

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