Mixed Markov Process And Its Application In Cognitive Radios

The state transition procession of continuous time random process, satisfyingthe Markov properties, must adjust to an exponential distribution. In the practicalapplication of engineering, we often encounter some random processes without theMarkov properties, which are similar with the stochastic process with the Markovproperties. Consequently, in order to expand the applied range of Markov process,it is necessary to relax the constraint conditions of the Markov process.In cognitive radio network, the primary users have the priority to access thespectrum resources, and secondary users can make opportunistic use of the idlespectrum to enhance the utilization of spectrum resource. At the moment whenprimary users access some spectrum, secondary users give up these spectrum andleave. During the process, secondary users can enter the system queue and wait foridle spectrum. In this paper, the numerical simulation comparisons between themathematical model with exponential backoff dynamic spectrum access and onewith the constant backoff dynamic spectrum access illustrate that the latter is betterin term of quality of secondary users. However, the constant backoff dynamicspectrum access cannot be described as the traditional Markov process. Among theexisting theoretical scope, the steady-state probability has not been solved. As aresult, the dropped calls rate and completed calls rate cannot be obtained as well.An innovative random process-mixed Markov process is proposed to solve theabove problems. By studying of mixed Markov process, we propose the firstrepresentation pattern of mixed Markov process and its calculation method. Inaddition, with the observation of the relationship of rate and the variation trend ofsteady-state with the time-T, we find some features of mixed Markov process aredifferent with the continuous Markov process, which explain why the quality ofsecondary users of the dynamic spectrum access model with the constant backoff isdifferent from the one with exponential backoff. After that, we introduce thesecond representation method of mixed Markov process. Since that accumulationwith the expected exponential distribution constitutes a gamma distribution, on thecondition that the expected T constant is unchanged, with the accumulation ofexponential distributions, the gamma distribution will eventually become the deltadistribution. In this way, the spending time of secondary users becomes a constant.From another perspective, the finding allows us to cut the constant backoff processinto many small possion processes, by which a continuous Markov process can bebuilt. Through the comparisons between the theoretical and experimental values, we found the speed, that theoretical values approximate the experimental, is fastwith the increases of cutting number.As a derived class of Markov process, the researches of mixed Markovprocess are of great significance in the mathematical theory and engineeringapplications fields.