Semi-Markov-Based Approach for the Analysis of Open Tandem Networks with Blocking and Truncation

Abstract

This paper describes an analytical study of open two-node (tandem) network models with blocking and truncation. The study is based on semi-Markov process theory, and network models assume that multiple servers serve each queue. Tasks arrive at the tandem in a Poisson fashion at the rate λ, and the service times at the first and the second node are nonexponentially distributed with means s A and s B , respectively. Both nodes have buffers with finite capacities. In this type of network, if the second buffer is full, the accumulation of new tasks by the second node is temporarily suspended (a blocking factor) and tasks must wait on the first node until the transmission process is resumed. All new tasks that find the first buffer full are turned away and are lost (a truncation factor). First, a Markov model of the tandem is investigated. Here, a twodimensional state graph is constructed and a set of steady-state equations is created. These equations allow calculating state probabilities for each graph state. A special algorithm for transforming the Markov model into a semi-Markov process is presented. This approach allows calculating steady-state probabilities in the semi-Markov model. Next, the algorithms for calculating the main measures of effectiveness in the semi-Markov model are presented. In the numerical part of this paper, the author investigates examples of several semi-Markov models. Finally, the results of calculating both the main measures of effectiveness and quality of service (QoS) parameters are presented.

Service Strategies in Two-Server Tandem Configurations – Modeling and Investigation

“…In particular, the two-node tandem queuing model with the Batch Markovian Arrival Process input flow and non-exponential service time distribution described in the paper [8]. Additionally, systems with finite capacity queues under various blocking mechanisms and scheduling constraints are analyzed by the author in [15][16][17][18][19][20][21][22][23][24][25]. In [15,16], the closed type, multi-center computer networks with different blocking strategies are investigated and measures of effectiveness based on Quality of Service (QoS) are studied.…”

“…In [15,16], the closed type, multi-center computer networks with different blocking strategies are investigated and measures of effectiveness based on Quality of Service (QoS) are studied. Markovian and semi-Markovian approaches for analysis of open tandem networks with blocking are presented in [17], [19], [21], [23] [24] and [25]. Some two-stage tandem queues with blocking and an optional feedback are presented in [20] and [22].…”

Tandem Communication Network Model with DBA having Non Homogeneous Poisson arrivals and Feedback for First Node

“…According to [9] [10], networks that support tele-processing applications are mixed with dynamic engineering skills and statistical multiplexing. To improve the quality of service in transmission, several authors have studied the communication networks utilizing tandem queuing analogy [11], [12], [13]. The performance evaluation of a two node communication network with dynamic bandwidth allocation and modified phase type transmission having bulk arrivals is studied in [14].…”