• Journal of Korea Society of Industrial Information Systems
• /
• v.29 no.1
• /
• pp.63-76
• /
• 2024

In this study, we analyzed queue length and sojourn time of discrete-time BMAP/G/1 queues under the workload control. Group customers (packets) with correlations arrive at the system following a discrete-time Markovian arrival process. The server starts busy period when the total service time of the arrived customers exceeds a predetermined workload threshold D and serves customers until the system is empty. From the analysis of workload and waiting time, distributions of queue length at the departure epoch and arbitrary time epoch and system sojourn time are derived. We also derived the mean value as a performance measure. Through numerical examples, we confirmed that we can obtain results represented by complex forms of equations, and we verified the validity of the theoretical values by comparing them with simulation results. From the results, we can obtain key performance measures of complex systems that operate similarly in various industrial fields and to analyze various optimization problems.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.22 no.9
• /
• pp.2027-2034
• /
• 1997

Frame relay is a fast packet switching technology that performs relaying and multiplexing frames with variable lengths over a wide area link at the T1 or E1 speed, by elminating error and flow control in the network. In frame relay networks, congestion control is typically performed through the rate enforcement with a discard eligibility (DE) bit, and the explicit negative feedback meachanisms using explicit congetion notification bits. In this paper, we consider the congestiong control scheme using the rate enforcement mechanism with DE bit for frame relay network. Assuming that each frame with exponentially distributed length arrives according to the Poission fashion, we can treat the frame relay switch as an M/M/1/K priority queueing system with pushout basis. We analyze and present the blocking probabilities and waiting time distributions of frames.