Rejoinder on: queueing models for the analysis of communication systems

In this rejoinder, we respond to the comments and questions of three discussants of our paper on queueing models for the analysis of communication systems. Our responses are structured around two main topics: discrete-time modeling and further extensions of the presented queueing analysis

Queues with Galton-Watson-type arrivals

This paper presents the analysis of a discrete-time single server queueing system with a multi-type Galton-Watson arrival process with migration. It is shown that such a process allows to capture intricate correlation in the arrival process while the corcesponding queueing analysis yields closed-form expressions for various moments of queue content and packet delay

Cost minimization for unstable concurrent products in multi-stage production line using queueing analysis

This research and resulting contribution are results of Assumption University of Thailand. The university partially supports financially the publication.Purpose: The paper copes with the queueing theory for evaluating a muti-stage production line process with concurrent goods. The intention of this article is to evaluate the efficiency of products assembly in the production line. Design/Methodology/Approach: To elevate the efficiency of the assembly line it is required to control the performance of individual stations. The arrival process of concurrent products is piled up before flowing to each station. All experiments are based on queueing network analysis. Findings: The performance analysis for unstable concurrent sub-items in the production line is discussed. The proposed analysis is based on the improvement of the total sub-production time by lessening the queue time in each station. Practical implications: The collected data are number of workers, incoming and outgoing sub-products, throughput rate, and individual station processing time. The front loading place unpacks product items into concurrent sub-items by an operator and automatically sorts them by RFID tag or bar code identifiers. Experiments of the work based on simulation are compared and validated with results from real approximation. Originality/Value: It is an alternative improvement to increase the efficiency of the operation in each station with minimum costs.peer-reviewe

Application of Tauberian Theorem to the Exponential Decay of the Tail Probability of a Random Variable

We give a sufficient condition for the exponential decay of the tail probability of a non-negative random variable. We consider the Laplace-Stieltjes transform of the probability distribution function of the random variable. We present a theorem, according to which if the abscissa of convergence of the LS transform is negative finite and the real point on the axis of convergence is a pole of the LS transform, then the tail probability decays exponentially. For the proof of the theorem, we extend and apply so-called a finite form of Ikehara's complex Tauberian theorem by Graham-Vaaler.Comment: 22pages, 1 figure, submitted to IEEE Transactions on Information Theor

Queueing analysis of a canonical model of real-time multiprocessors

A logical classification of multiprocessor structures from the point of view of control applications is presented. A computation of the response time distribution for a canonical model of a real time multiprocessor is presented. The multiprocessor is approximated by a blocking model. Two separate models are derived: one created from the system's point of view, and the other from the point of view of an incoming task