Queueing Systems

, Volume 71, Issue 3, pp 293-320

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

A performance analysis of channel fragmentation in dynamic spectrum access systems

  • Ed CoffmanAffiliated withElectrical Engineering, Columbia University
  • , Philippe RobertAffiliated withINRIA Paris-Rocquencourt
  • , Florian SimatosAffiliated withCWI Email author 
  • , Shuzo TarumiAffiliated withElectrical Engineering, Columbia University
  • , Gil ZussmanAffiliated withElectrical Engineering, Columbia University


Dynamic Spectrum Access systems offer temporarily available spectrum to opportunistic users capable of spreading transmissions over a number of non-contiguous subchannels. Such methods can be highly beneficial in terms of spectrum utilization, but excessive fragmentation degrades performance and hence off-sets the benefits. To get some insight into acceptable levels of fragmentation, we present experimental and analytical results derived from a mathematical model. According to the model, a system operates at capacity serving requests for bandwidth by assigning a collection of one or more gaps of unused bandwidth to each request as bandwidth becomes available. Our main result is a proof that, even if fragments can be arbitrarily small, the system remains stable in the sense that the average total number of fragments remains bounded. Within the class of dynamic fragmentation models, including models of dynamic storage allocation that have been around for many decades, this result appears to be the first of its kind.

In addition, we provide extensive experimental results that describe behavior, at times unexpected, of fragmentation as parameter values are varied. Different scanning rules for searching gaps of available spectrum, all covered by the above stability result, are also studied. Our model applies to dynamic linked-list storage allocation, and provides a novel analysis in that domain. We prove that, interestingly, a version of the 50 % rule of the classical, non-fragmented allocation model holds for the new model as well. Overall, the paper provides insights into the behavior of practical fragmentation algorithms.


Dynamic spectrum access Fragmentation Ergodicity of Markov chains Cognitive radio Lyapunov function

Mathematics Subject Classification