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# Maximizing throughput in wireless networks via gossiping

Measurement and Modeling of Computer Systems, no. 1 (2006): 27-38

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Abstract

A major challenge in the design of wireless networks is the need for distributed scheduling algorithms that will efficiently share the common spectrum. Recently, a few distributed al- gorithms for networks in which a node can converse with at most a single neighbor at a time have been presented. These algorithms guarantee 50% of the maxim...More

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Introduction

- One of the major challenges in the design and operation of wireless networks is to schedule transmissions to efficiently share the common spectrum among links in the same geographic area.
- In the context of switch scheduling and node-exclusive spectrum sharing networks, this algorithm has to schedule the edges of the Maximum Weight Matching at each time slot, where the edge weights are the queue sizes.
- For the simplicity of presentation, in sections 4 and 5 the authors assumed that (i) the running time of the New-Sch and the Mix algorithms is shorter than the slot used for data transmission and (ii) all nodes make the decision in Step 1.iii of the Merge algorithm simultaneously.

Highlights

- One of the major challenges in the design and operation of wireless networks is to schedule transmissions to efficiently share the common spectrum among links in the same geographic area
- We show that if the difference between the preferable matching and the selected matching is bounded with high probability, the system is stable for any set of rates (1 − α − β)Λ∗, where Λ∗ is the stability region under a perfect scheduler. α and β are small constants that depend on the allowed difference between the preferable and selected matchings and on the probability that a maximum weight matching will be selected
- This paper presents the first distributed scheduling algorithms for wireless networks that obtain 100% throughput
- We have shown that even if the merge procedure sometimes results in an inferior matching, under certain conditions the throughput will still be nearly 100%
- Based on this framework and on the observation that the required information can be collected within local components, we have developed a few distributed algorithms including a very efficient gossip algorithm
- The presented framework can be extended to general interference constraints

Results

- (2) Use Rand-Match for constant number of iterations to obtain a matching on the graph Gm. The authors state the following straightforward result about the Arr-Match algorithm.
- It is desirable to develop a distributed approximation algorithm for the maximum weight matching problem that satisfies property P1 with relatively large δ.
- In the summation algorithm presented in Section 5.1, if a connected component of G1 is a path, the two nodes at both ends of the path will indicate it in the messages they send.
- The gossip algorithms presented in Sections 5.2 and 5.3 can operate well without special messages initiated by nodes at the ends of a path.
- The combination of the Rand-Match and the summation algorithms will result in a network which is stable for all rates within the stability region Λ∗.
- In [6, 17] it has been shown that for the node-exclusive spectrum sharing model, using a maximal matching algorithm to schedule the transmissions allows to obtain at least 0.5 of the stability region.
- Notice that for all the algorithms discussed above, the time complexities were obtained assuming that at each time slot, every node can send a single control message to all of its neighbors.
- This is a standard definition used for comparing the performance of different distributed algorithms, it does not adhere to the specific characteristics of networks with primary interference constraints.
- The first required component is a distributed New-Sch algorithm that selects an independent set in the interference graph, such that the probability of selecting the maximum weight independent set is positive.

Conclusion

- This paper presents the first distributed scheduling algorithms for wireless networks that obtain 100% throughput.
- Some of the key issues in that context are: (i) how should the control messages be transmitted in a node-exclusive spectrum sharing model, (ii) what are the tradeoffs between throughput, delay, and decentralization costs, and (iii) how can the algorithms deal with an asynchronous network.
- The presented framework can be extended to general interference constraints

- Table1: Time complexity, communication complexity, local computation complexity, message size, addressing requirement, and stability region of the various algorithms (α and β are small constants)

Funding

- This work was supported by NSF ITR grant CCR-0325401, by ONR grant number N000140610064, and by DARPA/ AFOSR through the University of Illinois grant no
- The research of Gil Zussman was supported by a Marie Curie International Fellowship within the 6th European Community Framework Programme

Reference

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