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The problem of compressed sensing (CS) based multiple access is studied under the assumption of random data traffic. In many multiple access systems, i.e., wireless sensor networks (WSNs), data arrival is random due to the bursty data traffic for every transmitter. Following the recently developed CS methodology, the technique of compressing the transmitter identities into data transmissions is proposed, such that it is unnecessary for a transmitter to inform the base station its identity and its request to transmit. The proposed compressed multiple access scheme identifies transmitters and recovers data symbols jointly. Numerical simulations demonstrate that, compared with traditional multiple access approaches like carrier sense multiple access (CSMA), the proposed CS based scheme achieves better expectation and variance of packet delays when the traffic load is not too small.