Optimal static pricing for a tree network

Abstract

We study the static pricing problem for a network service provider in a loss system with a tree structure.In the network, multiple classes share a common inbound link and then have dedicated outbound links.The motivation is from a company that sells phone cards and needs to price calls to different destinations.We characterize the optimal static prices in order to maximize the steady-state revenue. We report new structural findings as well as alternative proofs for some known results. We compare the optimal static prices versus prices that are asymptotically optimal, and through a set of illustrative numerical examples we show that in certain cases the loss in revenue can be significant. Finally, we show that static prices obtained using the reduced load approximation of the blocking probabilities can be easily obtained and have near-optimal performance, which makes them more attractive for applications.

Congestion probabilities in OFDM wireless networks with compound Poisson arrivals

“…[34] refer to the problem of the CBP determination in circuit‐switched networks, see e.g. [35, 36]. More specifically, the algorithms in [33] are based on mean‐value analysis and z ‐transforms.…”

Bulletin of the Polish Academy of Sciences: Technical Sciences

“…In [16], Paik and Suh propose the algorithms from [25] and [26] for the determination of G(P − p k b l , M − b l ) (and consequently for the CBP calculation of B(k, l)) without providing Performance metrics in OFDM wireless networks supporting quasi-random traffic explicit details. The algorithms of [25] and [26] are proposed in the literature for the CBP determination in circuit-switched networks (see e.g., [27,28]). The algorithms from [25] are based on z-transforms and mean-value analysis.…”

Revenue management on an on-demand service platform

“…Ziya et al (2006) considers the optimal pricing problem faced by a service facility with a single server and a queue with a finite capacity (which could be 0, as in our setting), when the customer valuations are drawn from a common distribution. Both Ziya et al (2008) and Caro and Simchi-Levi (2012) analyze the case of multiple heterogeneously distributed customer classes in a similar setting. Although these settings are more general, the more focused analysis of the setting without queueing in the present work, motivated by on-demand platforms, results in several novel results and insights that do not hold in the general setting.…”

“…The present work is closely related to the literature on pricing in service systems; see Hassin and Haviv (2003) for a survey. Three works most relevant to the present setting are Ziya et al (2006), Ziya et al (2008) and Caro and Simchi-Levi (2012). Ziya et al (2006) considers the optimal pricing problem faced by a service facility with a single server and a queue with a finite capacity (which could be 0, as in our setting), when the customer valuations are drawn from a common distribution.…”