Channel Holding Time Distribution in Cellular Telephony

The duration of the holding time (dwell-time) in cellular telephony systems is a fraction of the total call duration due to the handoff mechanism. Some elements such as the mobility and cell shape and size will cause the dwell-time to have a probability distribution function different to that of the call duration, being the difference greater for higher mobility and smaller cell sizes (the limit is for stopped mobile units and/or very large cell size, then the dwell-time is equal to the call duration). Several authors have tried to model the channel holding time making use of analytical tools and/or simulations [ZON, RAP, STE, GUE, HON]. All these studies assume the negative exponential distribution for the uncumbered call duration because analytical results for other distributions become highly complex or impossible to attain and the use of the exponential distribution for the call holding time is widely spread in the teletraffic field. From this starting point all the above mentioned studies get to the conclusion that the channel holding time is also distributed according to a negative exponential (obviously with smaller average). Surprisingly this conclusion is reached by assuming different assumptions for mobility, cell size and shape, speed, etc.