Markov Chain for Multihop WSN



  1. propose a Markov chain-based analytical framework for modeling the behavior of the medium access control (MAC) protocol in IEEE 802.15.4 multihop wireless sensor networks
  2. Extend the framework proposed in “I. Ramachandran, A. K. Das, and S. Roy, “Analysis of the contention access period of IEEE 802.15.4 MAC,” ACM Trans. Sensor Networks, vol. 3, no. 1, 29 pages” to 2-hop network scenario.


  1. Their framework can be generalized to evaluate the performance of multihop networks with arbitrary complex topologies (e.g., mesh networks or networks with multiple sinks), where the relays may contend the access medium to the remote sensor nodes.
  2. No ACK messages are considered.
  3. The probability that a node begins its transmission in any generic backoff slot can be approximated by the steady state probability.
  4. The number of backoff slots that a node has to wait in a backoff stage has a uniform distribution. However, in other research, this number is assumed to have a geometric distribution to take advantage of its memoryless property.
  5. When sensor is in IDLE state, it can generate data packets according to a poisson distribution and insert them in its buffer.
  6. The throughput is defined as the steady state probability of the SUCCESS state in the channel DMTC, and can be equivalently reinterpreted as the fraction of time spent in successful transmissions by each sensor.
  7. This paper using throughput formula from other reference paper.
  8. paper “Analysis of the contentionaccess period of IEEE 802.15.4 MAC” and “Performance of a beacon enabled IEEE 802.15.4 cluster with downlink and uplink traffic,”  are Main Reference of this paper for throughput and delay numerical analysis 1-hop.
  9. The authors modify the throughput and delay formula from 1-hop become 2-hop.

1. Steady state probability
2. Uniform distribution
3. Geometric distribution
4. Probability generating function (PGF)

1. Network throughput vs. pernode offered load (pck/sec)
2. Packet delivery delay vs. pernode offered load (pck/sec

Source :

Markov Chain-Based Performance Evaluation of IEEE 802.15.4 Multihop Wireless Sensor Networks. By Marco Martal`o, Gianluigi Ferrari, and Stefano Busanelli

Note : This resume is created for self-learning only. Author and Publisher hold copyrights


October 13, 2009
Taipei City – High Speed Network LabTaiwan Tech (NTUST)
Electronic Engineering Polytechnic Institute of Surabaya (EEPIS)

Udin Harun

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