1st International ICST Workshop on Spatial Stochastic Models for Wireless Networks

Research Article

M/D/1/1 loss system with interference and applications to transmit-only sensor networks

  • @INPROCEEDINGS{10.1109/WIOPT.2007.4480073,
        author={Bartlomiej  Blaszczyszyn and Bozidar Radunovic},
        title={M/D/1/1 loss system with interference and applications to transmit-only sensor networks},
        proceedings={1st International ICST Workshop on Spatial Stochastic Models for Wireless Networks},
        publisher={IEEE},
        proceedings_a={SPASWIN},
        year={2008},
        month={3},
        keywords={Interference  Performance analysis  Power system modeling  Propagation losses  Protocols  Rayleigh channels  Sensor systems  Sensor systems and applications  Signal to noise ratio  Wireless sensor networks},
        doi={10.1109/WIOPT.2007.4480073}
    }
    
  • Bartlomiej Blaszczyszyn
    Bozidar Radunovic
    Year: 2008
    M/D/1/1 loss system with interference and applications to transmit-only sensor networks
    SPASWIN
    IEEE
    DOI: 10.1109/WIOPT.2007.4480073
Bartlomiej Blaszczyszyn1,*, Bozidar Radunovic2,*
  • 1: INRIA & ENS and Mathematical Institute University of Wroclaw, 45 rue d'Ulm, 75005 Paris FRANCE.
  • 2: Microsoft Research, 7 JJ Thomson Avenue, Cambridge, CB3 OFB, UK
*Contact email: Bartek.Blaszczyszyn@ens.fr, bozidar@microsoft.com

Abstract

We propose and analyze a probabilistic model of packet reception in the steady state regime of a non-slotted wireless communication channel. It is an extension of the classical M/D/1/1 Erlang's loss model where the interference created by different packet emissions is introduced by means of a shot-noise process. More precisely, we assume that a given packet is admitted by the single receiver if this latter is idle at the packet arrival epoch and successfully received if, in addition, its signal-to-interference-and-noise ratio averaged over the reception period is large enough. As the main result we prove an analog of the Erlang's formula for the ergodic rate of the successfully received packets. Our work is motivated by some applications to transmit-only sensor networks.