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This paper investigates three joint call admission control algorithms (JCAC) for heterogeneous cellular networks. These algorithms are random-selection-based, service-based, and load-based JCAC algorithms. Our approach is based on decomposing heterogeneous cellular networks into groups of co-located cells. We model the JCAC algorithms as a multi-dimensional Markov chain. For each of the three JCAC algorithms, new call blocking probability and handoff call probability are derived and evaluated. The performances of the three JCAC algorithms are compared and the results are presented.