Reliable transfer of a data buffer window over lossy wireless channels may require many retransmissions. Due to high power consumption of radio hardware and delay constraints of real time applications, wireless link protocols operating at resource poor environments aim to minimize the number of these retransmissions. In this paper, we consider reliable broadcast of the full buffer in a window to multiple recipients over wireless channels. We present a generic sender initiated negative acknowledgement based joint retransmission scheme and its mathematical analysis in terms of the total number of packets transmitted in a reliable transfer session. In the analysis, we assume that the communication channels have independent packet loss probabilities. Hence, some packets may successfully be received by only a subset of the receivers. The analysis concludes with a generalized formula derived as a function of number of receivers (k) and buffer size (N). The formula, which is also verified with simulations, can be useful as a basis for the theoretical analysis of joint retransmission based cooperative Automatic-Request-Reply (ARQ) protocols.