Determining the optimal buffer size for short message transfer in a heterogeneous GPRS/UMTS network

Multimedia messaging service (MMS) enables the transmission of messages with full content versatility between mobile devices and from applications to these devices, which can be used over the general packet radio service (GPRS)/universal mobile telecommunications system (UMTS) short message service (SMS) network. In the GPRS/UMTS SMS network, the serving GPRS support node (SGSN) stores the mobile-terminated message in a queue until it is successfully transferred to the mobile device or its maximum waiting time expires. If the mobile device moves from one SGSN area to another before the waiting time has expired, the queued message is forwarded to the new SGSN and is immediately removed from the waiting queue of the old SGSN. Taking the forwarding and the expiration effects of queued messages into account, the paper develops an analytical model to study the system performance of a heterogeneous GPRS/UMTS SMS network, in which the parameters (e.g., message arrival rate, SGSN area residence time, buffer size, etc.) of SGSNs can be varied. On the basis of the analytical model, an iterative method is proposed to determine the optimal buffer size so that the available bandwidth is fully utilized and the message loss probability is minimized.