On the serial correlation for number in system in the stationary GI/M/1 bulk arrival and GI/Em/1 queues

1992 ◽  
Vol 29 (2) ◽  
pp. 404-417
Author(s):  
D. A. Stanford ◽  
B. Pagurek
Keyword(s):  
Correlation Coefficient ◽  
Generating Functions ◽  
Serial Correlation ◽  
Correlation Coefficients ◽  
Numerical Examples ◽  
Bulk Arrival ◽  
Serial Correlation Coefficient ◽  
Infinite Sum

The generating functions for the serial covariances for number in system in the stationary GI/M/1 bulk arrival queue with fixed bulk sizes, and the GI/Em/1 queue, are derived. Expressions for the infinite sum of the serial correlation coefficients are also presented, as well as the first serial correlation coefficient in the case of the bulk arrival queue. Several numerical examples are considered.

On the serial correlation for number in system in the stationary GI/M/1 bulk arrival and GI/Em /1 queues

1992 ◽  
Vol 29 (02) ◽  
pp. 404-417
Author(s):  
D. A. Stanford ◽  
B. Pagurek
Keyword(s):  
Correlation Coefficient ◽  
Generating Functions ◽  
Serial Correlation ◽  
Correlation Coefficients ◽  
Numerical Examples ◽  
Bulk Arrival ◽  
Serial Correlation Coefficient ◽  
Infinite Sum

The generating functions for the serial covariances for number in system in the stationary GI/M/1 bulk arrival queue with fixed bulk sizes, and the GI/Em /1 queue, are derived. Expressions for the infinite sum of the serial correlation coefficients are also presented, as well as the first serial correlation coefficient in the case of the bulk arrival queue. Several numerical examples are considered.

A Note on Serial Correlation Coefficients and Related Characterizations of Gamma and Exponential Distributions

1972 ◽  
Vol 21 (1-2) ◽  
pp. 57-62 ◽  
Author(s):  
D. N. Shanbhag ◽  
I. V. Basawa
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Normality ◽  
Correlation Coefficient ◽  
Serial Correlation ◽  
Correlation Coefficients ◽  
Exponential Distributions ◽  
The Central Limit Theorem ◽  
Independent Observations ◽  
Serial Correlation Coefficient

Summary Some properties of the distribution of the serial correlation coefficient based on a sample of independent observations and that of a certain related statistic are used to characterize gamma and exponential distributions. Also, a certain extension of the central limit theorem is given which may be useful in establishing the asymptotic normality of serial correla­ tion­type statistics.

A queueing system with Markov-dependent arrivals

1985 ◽  
Vol 22 (03) ◽  
pp. 668-677 ◽  
Author(s):  
Pyke Tin
Keyword(s):  
Special Reference ◽  
Correlation Coefficient ◽  
Waiting Time ◽  
Serial Correlation ◽  
Queueing System ◽  
Arrival Process ◽  
Single Server ◽  
Queue Size ◽  
Interarrival Times ◽  
Serial Correlation Coefficient

This paper considers a single-server queueing system with Markov-dependent interarrival times, with special reference to the serial correlation coefficient of the arrival process. The queue size and waiting-time processes are investigated. Both transient and limiting results are given.

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