Optimal Sleeping Mechanism for Multiple Servers with MMPP-Based Bursty Traffic Arrival

TL;DR

This paper establishes the optimal hysteretic, queue-threshold-based sleeping policy for multiple servers under bursty MMPP traffic, optimizing energy-delay tradeoffs in green communication networks.

Contribution

It proves the optimal structure of sleep mechanisms for multiple servers with bursty MMPP arrivals, confirming a conjecture for single-server cases and providing numerical thresholds.

Findings

Optimal sleep policy is hysteretic and queue-threshold-based.

The policy is derived for multiple servers with bursty MMPP traffic.

Numerical solutions determine exact thresholds for implementation.

Abstract

An important fundamental problem in green communications and networking is the operation of servers (routers or base stations) with sleeping mechanism to optimize energy-delay tradeoffs. This problem is very challenging when considering realistic bursty, non-Poisson traffic. We prove for the first time the optimal structure of such a sleep mechanism for multiple servers when the arrival of jobs is modeled by a bursty Markov-modulated Poisson process (MMPP). It is shown that the optimal operation, which determines the number of active (or sleeping) servers dynamically, is hysteretic and monotone, and hence it is a queue-threshold-based policy. This work settles a conjecture in the literature that the optimal sleeping mechanism for a single server with interrupted Poisson arrival process, which can be treated as a special case of MMPP, is queue-threshold-based. The exact thresholds are given by numerically solving the Markov decision process.