Glauber dynamics are a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. Applications include distributed control algorithms for wireless networks. In this talk, we will present bounds on the mixing time of a generalization of Glauber dynamics where multiple sites are updated in each time slot and the fugacity of each site can be different. The results can be used to obtain conditions on system parameters such as fugacities, node degrees and node update probabilities, under which the mixing time grows polynomially in the number of sites.