In this paper, we study a system that adopts complete sharing admission policy to multiple broadband real-time variable bit rate (VBR) service sharing a common buffer or cache. Under joint connection-level and packet-level analysis, we utilize shared cache queue model with multiple ON-OFF sources to analyze the probability distribution of the number of packets and then obtain the formulas of calculating packet loss rate and average delay. Through numerical calculation, the results compared with the non-caching system indicate that the packet loss rate has decreased, but the average delay has increased. Taking into account the delay sensitive nature of real-time VBR service, this paper puts forward a call admission control (CAC) algorithm that gives consideration to both packet-level performance parameters and connection-level performance parameters. The algorithm optimizes the average delay of the system with constraints on call blocking probabilities for each kind of VBR service and a common packet loss rate for all services. Numerical examples exhibit the nature of such systems.