Loner Links Aware Routing and Scheduling in Wireless Mesh Networks Parth H. Pathak, Divya Gupta * and Rudra Dutta Department of Computer Science, North Carolina State University, Raleigh, NC, USA. * Microsoft Corporation, USA. Email: phpathak@ncsu.edu,{rdutta, dutta}@csc.ncsu.edu Abstract—In Wireless Mesh Networks (WMNs), TDMA based link scheduling can allow multiple concurrent transmissions, resulting in throughput improvements. In this paper, we identify certain link characteristics which reduce achieved spatial reuse and increase schedule length. It is shown that certain links (called loners) based on their length and position, introduce inherent difficulty in scheduling them with other links in network. Effects of such links on scheduling reveals important limitations of any such scheduling algorithm and motivates need of joint routing, scheduling and power control. We then present joint routing, topology control and scheduling algorithm to alleviate effects of loner links. Simulation results confirm throughput improvement with shorter schedule length. I. I NTRODUCTION AND PROBLEM DESCRIPTION Two contradicting power control strategies for WMNs are proposed by short-range multi-hop COMPOW [1] and long- range single-hop DirectTrans [2]. In COMPOW, all nodes use a uniform constant power level which is minimum required to maintain network connectivity. COMPOW achieves better concurrency in link scheduling but requires more number of transmissions per link with longer routing paths. In sharp contrast to this, in DirectTrans, nodes willing to transmit increase their power level until receiver can be reached in single hop. DirectTrans benefits from fewer transmissions and lower end-to-end delay but suffers with lower spatial reuse due to long higher interference links. WMNs can be modeled as communication graph G = (V,E), where V = {v 1 ,v 2 , ....v n } represents set of n mesh routers located based on any arbitrary distribution in Euclidean plane. Every node in the network has the ability to vary its transmission power level continuously over a wide range. In DirectTrans [2], every node willing to send data uses just enough transmission power to reach the receiver in single hop and topology may result into a clique. Every node in network has transmission range (RT ) and interference range (RI ) associated with it. With DirectTrans mechanism, RT xy reflects the length of an active transmission link xy and RI xy = σ · RT xy , where interference ratio σ> 1. We define and use following binary interference model in this work: 4−way Link Interference Model: Simultaneous transmis- sions on two links uv and xy results into collision-free data reception at the receivers if and only if d ux ,d uy ,d vx ,d vy > RI uv and d ux ,d uy ,d vx ,d vy > RI xy . This assures that transmission on two links do not interfere with each other, if and only if nodes u, v and x, y do not lie inside Interference Double Disks (D RI x xy ) ∪ (D RI y xy ) and (D RI u uv ) ∪ (D RI v uv ), respectively. Size of the Double Disk depends on RT which in turn depends on length of the link in DirectTrans mechanism. Traffic matrix Tr is n × n matrix in which a non-zero element Tr ij denotes end-to-end traffic demand between source i and destination j . Once, central controller performs routing using Tr, it reduces to a per link transmission demand matrix, Tx (also edge set E) which is used for TDMA link scheduling. Link quality and transmission data rates are assumed to be unvarying and identical. As shown in [2], decreasing average hop count using per- link-minimality condition is favorable for throughput and de- lay optimization in practical size networks. So, it is of foremost interest to design a scheduling algorithm for DirectTrans and extend it for joint routing and scheduling. In this work, we show that using DirectTrans mechanism introduces certain longer links in topology which limit reduction of schedule length below a certain limit. We characterize these loner links and investigate their impact on a scheduling algorithm. As shown in Fig. 1(a)., problems of power control, scheduling and routing are interrelated and should be addressed together. We study these interrelated problems for DirectTrans mechanism to eliminate the adverse effects of loner links. II. SCHEDULING ALGORITHM If transmissions on two links interfere with each other, they should not be schedule in parallel in the same slot. For better spatial reuse and higher throughput, a scheduling algorithm should try to schedule as many links as possible in every slot. To capture the interference relationship between links, conflict graph (G c ) can be derived from communication graph G. G c can be constructed by having a vertex for each edge of G. Any two vertices in G c have an edge between them, if and only if their corresponding links in G interfere with each other. Problem of finding conflict-free schedule in G is then similar to problem of finding maximum independent set in G c . In this section, we present a heuristic-based greedy algorithm for link scheduling which determines conflict-free feasible transmission schedule under 4−way link interference model. Every link can be associated with an interference score which is the number of other links with whom it interferes and hence can not be scheduled simultaneously. Greedy Scheduler shown in Algorithm 1 takes link transmis- sion matrix and conflict graph as inputs and outputs a conflict- free schedule of link transmissions. For every slot, scheduler first chooses base link for transmission by Criterion 1. Once base link is selected, all link transmissions interfering with it are postponed for future slots. Remaining set of links still have the opportunity to be scheduled with base link in current slot. Out of these candidate links, another link is chosen by Criterion 2. This process is repeated until no more links can be scheduled in parallel in current slot. Maximum interference score is used as 1 st and 2 nd Criterions which selects links with highest interference score from remaining links in every step.