# Partial Server Pooling in Redundancy Systems

## TL;DR

This paper investigates how partial resource sharing combined with redundancy in multi-server systems affects performance, proposing models for different redundancy policies and analyzing optimal sharing configurations.

## Contribution

It introduces models for partial sharing with redundancy in multi-server queues and analyzes the Pareto efficiency and bargaining solutions for sharing configurations.

## Key findings

- Full pooling is Pareto efficient for cancel-on-complete redundancy.
- At least one provider shares all resources in cancel-on-start redundancy.
- Sharing configurations can be optimized using bargaining theory.

## Abstract

Partial sharing allows providers to possibly pool a fraction of their resources when full pooling is not beneficial to them. Recent work in systems without sharing has shown that redundancy can improve performance considerably. In this paper, we combine partial sharing and redundancy by developing partial sharing models for providers operating multi-server systems with redundancy. Two M/M/N queues with redundant service models are considered. Copies of an arriving job are placed in the queues of servers that can serve the job. Partial sharing models for cancel-on-complete and cancel-on-start redundancy models are developed. For cancel-on-complete, it is shown that the Pareto efficient region is the full pooling configuration. For a cancel-on-start policy, we conjecture that the Pareto frontier is always non-empty and is such that at least one of the two providers is sharing all of its resources. For this system, using bargaining theory the sharing configuration that the providers may use is determined. Mean response time and probability of waiting are the performance metrics considered.