Queuing with Deterministic Service Times and No Waiting Lines in Machine Type Communications

TL;DR

This paper models queues with deterministic service times and no waiting lines in Machine-Type Communication, deriving bounds and approximations for blocking probability applicable to various queue scenarios.

Contribution

It introduces a novel queue model with deterministic service times and no waiting, extending to general distributions, with analytical bounds and approximations for blocking probability.

Findings

Derived simple bounds for blocking probability.

Provided a close approximation for blocking probability.

Validated results through simulations with Markovian and degenerate arrivals.

Abstract

The growth of Machine-Type Communication (MTC) increases the relevance of queuing scenarios with deterministic service times. In this letter, we present a model for queues without waiting lines and with degenerate service time distributions and show how the framework is extendable to model general service time distributions. Simple bounds and a close approximation of the blocking probability are derived and the results are shown to hold for simulated queues with Markovian and degenerate arrival processes.