I am struggling to understand how the probability value P is chosen for P-persistent CSMA for any particular station, what's the logic behind this.I have read from Wikipedia .


This approach lies between the 1-persistent and non-persistent CSMA access modes.[1] When the transmitting node is ready to transmit data, it senses the transmission medium for idle or busy. If idle, then it transmits immediately. If busy, then it senses the transmission medium continuously until it becomes idle, then transmits with probability p. If the node does not transmit (the probability of this event is 1-p), it waits until the next available time slot. If the transmission medium is not busy, it transmits again with the same probability p.

How the any station get highest probability and any probability value among the others on what basis?


2 Answers 2


So, this question actually asks two question:

  1. how to find the optimal value of p.
  2. given a value of p, how to set this value of p on any participating system.

For the first question: I would say that the probability p is chosen "experimentally" through modelling and/or simulation.

Throughput is decreased by both too low and too high values of p. If p is low, the probability of several stations accession channel at the same time is reduced. However, is p is too low, it may result in no station actually sending => empty time slot => lower throughput. If p is high, stations are likely to transmit. However, the probability of several stations attempting to transmit is higher, thus probability of collision increases, which also decreases throughput.

Here are the references I could find:

  1. L. Kleinrock and F. Tobagi: "Packet Switching in Radio Channels: Part I - Carrier Sense Multiple-Access Modes and Their Throughput-Delay Characteristics", 1975 (pdf)
  2. H. Takagi and L. Kleinrock: "Throughput Analysis for Persistent CSMA Systems", 1985 (pdf)

I admit, not the simplest math.

Some text-books include chapters on throughput analysis of Slotted ALOHA, CSMA/CD, which I think are based on the first paper.

For the second question, it should be specified in a standard Which gives us options.

  • Specify a value of p in a standard, then everyone can just hard-code it
  • Specify that p is a configuration parameter, which means that each system should be somehow configured with the value (I would say that this is bad protocol design)
  • Specify how stations can agree on the value of p. (example: in a context of wi-fi, one could specify that access point should tell stations their values of p).


  • The value of p is not necessarily fixed. A common strategy for backoffs on subsequent retransmissions is to start with p=1 and then reduce p each time there is a collision. (wikipedia)
  • Value of p is not necessary the same for each system. there are situations when we want to give priority to some stations. In this case one could assign larger values of p for systems with higher priority. The only accessible reference that I could find is this PhD thesis. If you have university access to IEEE and ACM, googling something like this could help: "Throughput Analysis of a p-Persistent CSMA Protocol with QoS Differentiation"
  • nowadays aloha is obsolete or using broadly? it's half-duplex?
    – S. M.
    Feb 20, 2022 at 20:49
  • P is same for all stations in one system?
    – S. M.
    Feb 22, 2022 at 6:01
  • in nowadays csma/cd broadly used or obsolete? Because in csma/cd not allowed more than one station to transmit, but present days more than one station can transmit at a time?
    – S. M.
    Feb 22, 2022 at 7:44
  • please reply p is same for all stations?
    – S. M.
    Feb 22, 2022 at 11:49
  • @AlokMaity regarding "same p" see second note
    – Effie
    Feb 22, 2022 at 14:32

Usually, the probability p for transmitting when a previously busy channel becomes free again is agreed upon by all nodes.

p is chosen by the installer mostly depending on the total number of nodes in the network and expected transmission rates, but also on the desired aggressiveness. E.g. when the number of nodes is more on the high side but the mean transmission rate is rather low (in respect of the network capacity), the installer may choose a higher aggressiveness (and higher p) to lower the expected latency. Effectively, p needs to be proportional to channel capacity / (number of nodes * their mean transmission demand) for best efficiency.

When one of the nodes 'cheats' by using a higher probability it gets a larger portion of the channel statistically. Increasing p or increasing the number of cheating system approaches a 1-persistent CSMA system.

  • You said it's the maximum probability... Maximum probability I know how to calculate.. I want to know how all stations get the their probability to transmit the data..
    – S. M.
    Sep 18, 2021 at 3:42
  • You said just probability for maximum success =1/n, n = total stations
    – S. M.
    Sep 18, 2021 at 10:37
  • No, it's the probability for transmitting at the beginning of a given time slot, not for success.
    – Zac67
    Sep 18, 2021 at 10:44
  • At P=1/n, we get maximum probability of success which is (1-1/n) ^n-1
    – S. M.
    Sep 18, 2021 at 11:26
  • 1
    p is not a probability of successful transfer; it's the probability of attempt to transfer to happen in the first place. Kinda like I can with great accuracy state the probability of myself throwing a dart in a crowded pub when space appears. I can't state the probability of a successful throw with any accuracy as I can't know whether another patron decides to stick his head in between the thrown dart and the board. Sep 19, 2021 at 15:48

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