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IEEE 802.16 standard specifies a contention based bandwidth request scheme for best-effort and non-real time polling services in point-to-multipoint (PMP) architecture. In this letter we propose an analytical model for the scheme and study how the performances of bandwidth efficiency and channel access delay change with the contention window size, the number of contending subscriber stations, the number of slots allocated for bandwidth request and data transmission. Simulations validate its high accuracy.