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In this paper, contention based bandwidth request with exponential increase and exponential decrease (EIED) backoff is suggested for WiMAX networks to overcome the limitations of truncated binary exponential backoff (TBEB) when contention is performed by accounting collision, channel error and unavailability of bandwidth. With EIED algorithm, the size of contention window is controlled (on collision or success) by varying the backoff factor with average contention window. The average contention window is derived by estimating the station's contention window size and accounting the transmission failure. The performance of contention resolution is studied by varying the number of stations, error rate and the number of slots available for transmission. The contention efficiency with EIED shows an improvement of 30.26% and 35.05% than TBEB with mutually exclusive and independent failure models, respectively. In addition, the access delay with EIED is reduced to 59% and 28.37% than TBEB with similar failure models.