Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Performing Load Balancing under Constraints

Andrea Fox, Francesco De Pellegrini, Eitan Altman, Arnob Ghosh, Ness Shroff

TL;DR

This work reframes load balancing under practical constraints as a constrained Markov decision process (CMDP), addressing both communication-rate limits and minimum-queue-activity requirements. It develops a near-optimal, Lyapunov-drift-based framework and introduces three lightweight safe policies—JSVED, JSED-$k$, and JSSQ—that guarantee constraint satisfaction while aiming to minimize system occupancy. The paper also extends these ideas to generic convex gain functions and validates performance through extensive simulations under light and heavy traffic, highlighting trade-offs between safety, memory demand, and scalability. The results offer scalable, provably safe strategies for constrained load balancing with potential applications in IoT, edge computing, and content delivery networks.

Abstract

Join-the-shortest queue (JSQ) and its variants have often been used in solving load balancing problems. The aim of such policies is to minimize the average system occupation, e.g., the customer's system time. In this work we extend the traditional load balancing setting to include constraints that may be imposed, e.g., due to the communication network. We cast the problem into the framework of constrained MDPs, enabling the consideration of both action-dependent constraints, such as, e.g, bandwidth limitation, and state-dependent constraints, such as, e.g., minimum queue utilization. Unlike the state-of-the-art approaches, our load-balancing policies, in particular JSED-$k$ and JSSQ, are both provably safe and yet strive to minimize the system occupancy. Their performance is tested with extensive numerical results under various system settings.

Performing Load Balancing under Constraints

TL;DR

This work reframes load balancing under practical constraints as a constrained Markov decision process (CMDP), addressing both communication-rate limits and minimum-queue-activity requirements. It develops a near-optimal, Lyapunov-drift-based framework and introduces three lightweight safe policies—JSVED, JSED-, and JSSQ—that guarantee constraint satisfaction while aiming to minimize system occupancy. The paper also extends these ideas to generic convex gain functions and validates performance through extensive simulations under light and heavy traffic, highlighting trade-offs between safety, memory demand, and scalability. The results offer scalable, provably safe strategies for constrained load balancing with potential applications in IoT, edge computing, and content delivery networks.

Abstract

Join-the-shortest queue (JSQ) and its variants have often been used in solving load balancing problems. The aim of such policies is to minimize the average system occupation, e.g., the customer's system time. In this work we extend the traditional load balancing setting to include constraints that may be imposed, e.g., due to the communication network. We cast the problem into the framework of constrained MDPs, enabling the consideration of both action-dependent constraints, such as, e.g, bandwidth limitation, and state-dependent constraints, such as, e.g., minimum queue utilization. Unlike the state-of-the-art approaches, our load-balancing policies, in particular JSED- and JSSQ, are both provably safe and yet strive to minimize the system occupancy. Their performance is tested with extensive numerical results under various system settings.

Paper Structure

This paper contains 21 sections, 6 theorems, 29 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Model
  3. The CMDP model
  4. Condition for the stability of the system
  5. Optimal policy properties
  6. Lyapunov optimization
  7. Finding a safe policy
  8. JSVED: Greedy policy w.r.t. virtual queues
  9. JSED-$k$: JSED with memory
  10. JSSQ: Join the Shortest Safe Queue
  11. Ensuring Resource Efficiency Through Minimum Occupation Constraints
  12. Numerical results
  13. Optimizing Lagrange multipliers
  14. Performance of JSED-$k$: different memory size
  15. Comparison performances of different safe policies
  16. ...and 6 more sections

Key Result

Proposition 1

For $\lambda \in \mathbb{R}^M$, $V \in \mathbb{R}$ and let $r^*$ the optimal reward we can obtain in this setting. There exists a greedy load-balancing policy $\tilde{\pi}$ such that time-average of the reward function $\overline{r}$ satisfies $\overline{r} \leq r^\star + O(1/V)$, and $\lim_{T \to \

Figures (5)

  • Figure 1: Load balancing for a parallel of $N$ queues with access constraint.
  • Figure 2: Average occupation and max cost of JSED-$k$ for increasing values of memory size $k$; light traffic conditions.
  • Figure 3: Evolution of the critical memory size at the increase of the number of queues.
  • Figure 4: Comparison of the policies described in \ref{['sec:safe policies']} for increasing ratio between arrival rate and capacity of the system.
  • Figure 5: Comparison of the reward and safety guarantees for different policies in the case of a convex generic gain function.

Theorems & Definitions (6)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Corollary 1
  • Theorem 1
  • Proposition 4