TY - GEN

T1 - Distributed online and stochastic queuing on a multiple access channel

AU - Bienkowski, Marcin

AU - Jurdzinski, Tomasz

AU - Korzeniowski, Miroslaw

AU - Kowalski, Dariusz R.

PY - 2012

Y1 - 2012

N2 - We consider the problems of online and stochastic packet queuing in a distributed system of n nodes with queues, where the communication between the nodes is done via a multiple access channel. In each round, an arbitrary number of packets can be injected into the system, each to an arbitrary node's queue. Two measures of performance are considered: the total number of packets in the system, called the total load, and the maximum queue size, called the maximum load. In the online setting, we develop a deterministic algorithm that is asymptotically optimal with respect to both complexity measures, in a competitive way. More precisely, the total load of our algorithm is bigger then the total load of any other algorithm, including centralized offline solutions, by only O(n 2), while the maximum queue size of our algorithm is at most n times bigger than the maximum queue size of any other algorithm, with an extra additive O(n). The optimality for both measures is justified by proving the corresponding lower bounds. Next, we show that our algorithm is stochastically optimal for any expected injection rate smaller or equal to 1. To the best of our knowledge, this is the first solution to the stochastic queuing problem on a multiple access channel that achieves such optimality for the (highest possible) rate equal to 1.

AB - We consider the problems of online and stochastic packet queuing in a distributed system of n nodes with queues, where the communication between the nodes is done via a multiple access channel. In each round, an arbitrary number of packets can be injected into the system, each to an arbitrary node's queue. Two measures of performance are considered: the total number of packets in the system, called the total load, and the maximum queue size, called the maximum load. In the online setting, we develop a deterministic algorithm that is asymptotically optimal with respect to both complexity measures, in a competitive way. More precisely, the total load of our algorithm is bigger then the total load of any other algorithm, including centralized offline solutions, by only O(n 2), while the maximum queue size of our algorithm is at most n times bigger than the maximum queue size of any other algorithm, with an extra additive O(n). The optimality for both measures is justified by proving the corresponding lower bounds. Next, we show that our algorithm is stochastically optimal for any expected injection rate smaller or equal to 1. To the best of our knowledge, this is the first solution to the stochastic queuing problem on a multiple access channel that achieves such optimality for the (highest possible) rate equal to 1.

UR - http://www.scopus.com/inward/record.url?scp=84868343490&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868343490&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-33651-5_9

DO - 10.1007/978-3-642-33651-5_9

M3 - Conference contribution

AN - SCOPUS:84868343490

SN - 9783642336508

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 121

EP - 135

BT - Distributed Computing - 26th International Symposium, DISC 2012, Proceedings

T2 - 26th International Symposium on Distributed Computing, DISC 2012

Y2 - 16 October 2012 through 18 October 2012

ER -