### Abstract

We consider a scheduling problem for a two-hop queueing network where the queues have randomly varying connectivity. Customers arrive at the source queue and are later routed to multiple relay queues. A relay queue can be served only if it is in connected state, and the state changes randomly over time. The source queue and relay queues are served in a time-sharing manner; that is, only one customer can be served at any instant. We propose Join the Shortest Queue-Longest Connected Queue (JSQ-LCQ) policy as follows: (1) if there exist nonempty relay queues in connected state, serve the longest queue among them; (2) if there are no relay queues to serve, route a customer from the source queue to the shortest relay queue. For symmetric systems in which the connectivity has symmetric statistics across the relay queues, we show that JSQ-LCQ is strongly optimal, that is, minimizes the delay in the stochastic ordering sense. We use stochastic coupling and show that the systems under coupling exist in two distinct phases, due to dynamic interactions among source and relay queues. By careful construction of coupling in both phases, we establish the stochastic dominance in delay between JSQ-LCQ and any arbitrary policy.

Original language | English |
---|---|

Article number | 4362652 |

Journal | Mathematical Problems in Engineering |

Volume | 2017 |

DOIs | |

Publication status | Published - 2017 Jan 1 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

### Cite this

**Delay-Optimal Scheduling for Two-Hop Relay Networks with Randomly Varying Connectivity : Join the Shortest Queue-Longest Connected Queue Policy.** / Baek, Seung Jun; Park, Joon Sang.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Delay-Optimal Scheduling for Two-Hop Relay Networks with Randomly Varying Connectivity

T2 - Join the Shortest Queue-Longest Connected Queue Policy

AU - Baek, Seung Jun

AU - Park, Joon Sang

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We consider a scheduling problem for a two-hop queueing network where the queues have randomly varying connectivity. Customers arrive at the source queue and are later routed to multiple relay queues. A relay queue can be served only if it is in connected state, and the state changes randomly over time. The source queue and relay queues are served in a time-sharing manner; that is, only one customer can be served at any instant. We propose Join the Shortest Queue-Longest Connected Queue (JSQ-LCQ) policy as follows: (1) if there exist nonempty relay queues in connected state, serve the longest queue among them; (2) if there are no relay queues to serve, route a customer from the source queue to the shortest relay queue. For symmetric systems in which the connectivity has symmetric statistics across the relay queues, we show that JSQ-LCQ is strongly optimal, that is, minimizes the delay in the stochastic ordering sense. We use stochastic coupling and show that the systems under coupling exist in two distinct phases, due to dynamic interactions among source and relay queues. By careful construction of coupling in both phases, we establish the stochastic dominance in delay between JSQ-LCQ and any arbitrary policy.

AB - We consider a scheduling problem for a two-hop queueing network where the queues have randomly varying connectivity. Customers arrive at the source queue and are later routed to multiple relay queues. A relay queue can be served only if it is in connected state, and the state changes randomly over time. The source queue and relay queues are served in a time-sharing manner; that is, only one customer can be served at any instant. We propose Join the Shortest Queue-Longest Connected Queue (JSQ-LCQ) policy as follows: (1) if there exist nonempty relay queues in connected state, serve the longest queue among them; (2) if there are no relay queues to serve, route a customer from the source queue to the shortest relay queue. For symmetric systems in which the connectivity has symmetric statistics across the relay queues, we show that JSQ-LCQ is strongly optimal, that is, minimizes the delay in the stochastic ordering sense. We use stochastic coupling and show that the systems under coupling exist in two distinct phases, due to dynamic interactions among source and relay queues. By careful construction of coupling in both phases, we establish the stochastic dominance in delay between JSQ-LCQ and any arbitrary policy.

UR - http://www.scopus.com/inward/record.url?scp=85038972024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038972024&partnerID=8YFLogxK

U2 - 10.1155/2017/4362652

DO - 10.1155/2017/4362652

M3 - Article

AN - SCOPUS:85038972024

VL - 2017

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

M1 - 4362652

ER -