To provide reliable connection management, a transport protocol uses 3-way handshakes in which user incarnations are identified by bounded incarnation numbers from some modulo-$N$ space. Cacheing schemes have been proposed to reduce the 3-way handshake to a 2-way handshake, providing the minimum latency desired for transaction-oriented applications. In this paper, we define a class of cacheing protocols and determine the minimum $N$ and optimal cache residency time as a function of real-time constraints (e.g.\ message lifetime, incarnation creation rate, inactivity duration, etc.). The protocols use the client-server architecture and handle failures and recoveries. Both clients and servers generate incarnation numbers from a local counter (e.g.\ clock). These protocols assume a maximum duration for each incarnation; without this assumption, there is a very small probability ($\approx \frac{1}{N^2}$) of misinterpretation of incarnation numbers. This restriction can be overcome with some additional cacheing. (Also cross-referenced as UMIACS-TR-93-24.1)