The technique of replica placement has been extensively employed to improve client perceived performance and disperse server workload. In this paper, we study some well-known algorithms of replica placement on the network and observe the logarithmic relationship between replica number and total access cost. Numerous simulations are done and it is found that some replica algorithms obey the logarithmic relationship with high correlation coefficients. A logrithmic function is proposed about replica number and total access cost. The logarithmic relationship is applied to the minimum facility problem and a function is deduced to get the optimal replica number.

Researchers have proposed numerous approaches to providing Quality-of-Service (QoS) across the Internet. The IETF has proposed two reservation approaches: hop-by-hop bandwidth reservation (IntServ); and per-hop behaviour bandwidth reservation (DiffServ). An edge router generates traffic, accepts per-flow reservation and classifies them into predetermined service class; while a core router ensures different QoS guarantees for each service class. We propose an Edge-to-Edge Quality-of-Service Domain in which packet trains with the same service requirements aggregated using packet deadline at edge router. The properties of a packet train like Inter-Packet Departure Time, Inter-flow Departure Time and accumulated packet delay are embedded and used by our quantum-based scheduler and QoS packet forwarding scheme in core routers. Thus, we are able to extract per-queue and per-flow information. Each queue is reconstructed at core router with packets having an expected departure time that is relative to the ingress router. Useful functions like instantaneous service rate and fine granular dropping scheme can be derived with a combination of embedded information and relative virtual clock technique. The encapsulation of our packet train information converges mathematically. Through simulations, we show that our architecture can provide delay and rate guarantees and minimise jitter for QoS-sensitive flows that requires LR-coupled or LR-decoupled reservations.