Queue occupancy and server size distribution of a queue length dependent vacation queue with an optional service
Ashish Verma, Sourav Pradhan

TL;DR
This paper models a discrete-time queue with batch arrivals, vacations, and two-phase service, providing detailed joint distributions and sensitivity analysis relevant to modern telecommunication systems like 5G and IoT.
Contribution
It introduces a comprehensive analytical framework for a queue with batch arrivals, vacations, and two-phase service, including joint distributions and numerical illustrations.
Findings
Derived joint probability generating functions for queue states
Established complete joint distribution at arbitrary times
Performed sensitivity analysis on key system parameters
Abstract
The discrete time queueing system is highly applicable to modern telecommunication systems, where it provides adaptive packet handling, congestion controlled security/inspection, energy efficient operation, and supports bursty traffic common in 5G, Internet of Things (IoT), and edge computing environments. In this article, we analyze an infinite-buffer discrete-time batch-arrival queue with single and multiple vacation policy where customers are served in batches, in two phases, namely first essential service (FES) and second optional service (SOS). In such systems, the FES corresponds to basic data processing or packet routing, while SOS represents secondary tasks such as encryption, error checking, data compression, or deep packet inspection that may not be necessary for every packet. Here, we derive the bivariate probability generating functions for the joint distribution of the…
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Taxonomy
TopicsAdvanced Queuing Theory Analysis · Advanced Wireless Network Optimization · Network Traffic and Congestion Control
