Performance Analysis of a Polling Model With BMAP and Across-Queue State-Dependent Service Discipline

As various video services become popular, video streaming will dominate the mobile data traffic. The H.264 standard has been widely used for video compression. As the successor to H.264, H.265 can compress video streaming better, hence it is gradually gaining market share. However, in the short term H.264 will not be completely replaced, and will co-exist with H.265. Using H.264 and H.265 standards, three types of frames are generated, and among different types of frames exist dependencies. Since the radio resources are limited, using dependencies and quantities of frames in buffers, an appropriate time division transmission policy can be applied to transmit different types of frames sequentially, in order to avoid the occurrence of video carton or decoding failure. Polling models with batch Markovian arrival process (BMAP) and across-queue state-dependent service discipline are considered to be effective means in the design and optimization of appropriate time division transmission policies. However, the BMAP and across-queue state-dependent service discipline of the polling models lead to the large state space and several coupled state transition processes, which complicate the performance analysis. There have been very few researches in this regard. In this paper, a polling model of this type is analyzed. By constructing a supplementary embedded Markov chain and applying the matrix-analytic method based on the semi-regenerative process, the expressions of important performance measures including the joint queue length distribution, the customer blocking probability and the customer mean waiting time are obtained. The analysis will provide inspiration for analyzing the polling models with BMAP and across-queue state-dependent service discipline, to guide the design and optimization of time division transmission policies for transmitting the video compressed by H.264 and H.265.