Stochastic Clearing Systems with Multiple Input Processes

TL;DR

This paper analyzes stochastic clearing systems with multiple Brownian motion inputs, proposing optimal policies and methods to evaluate average weighted delay, demonstrating the superiority of instantaneous rate policies over others.

Contribution

It introduces an optimal instantaneous rate policy for multi-input stochastic clearing systems and a unified method to evaluate delay under various policies.

Findings

Instantaneous rate policy is optimal among renewal policies.

The proposed method calculates average weighted delay under different policies.

Instantaneous rate and hybrid policies outperform time-based policies.

Abstract

In this paper, we consider stochastic clearing systems with multiple drifted Brownian motion inputs. First, we propose an instantaneous rate policy, which is shown to be the optimal one among a large class of renewal type clearing policies in terms of average cost. Second, we propose a service measure about average weighted delay rate, and provide a unified method to calculate the service measure under different clearing policies. Moreover, we prove that under a fixed clearing frequency, the instantaneous rate policy outperforms a large class of clearing policies, and the instantaneous rate hybrid policy performs better than time-based policy, in terms of average weighted delay rate.