Service and price competition when customers are naive

We consider a system of two service providers each with a separate queue. Customers choose one queue to join upon arrival and can switch between queues in real time before entering service to maximize their spot utility, which is a function of price and queue length. We characterize the steady-state distribution for queue lengths, and then investigate a two-stage game in which the two service providers first simultaneously select service rates and then simultaneously charge prices. Our results indicate that neither service provider will have both a faster service and a lower price than its competitor. When price plays a less significant role in customers service selection relative to queue length or when the two service providers incur comparable costs for building capacities, they will not engage in price competition. When price plays a significant role and the capacity costs at the service providers sufficiently differ, they will adopt substitutable competition instruments: the lower cost service provider will build a faster service and the higher cost service provider will charge a lower price. Comparing our results to those in the existing literature, we find that the service providers invest in lower service rates, engage in less intense price competition, and earn higher profits, while customers wait in line longer when they are unable to infer service rates and are naive in service selection than when they can infer service rates to make sophisticated choices. The customers jockeying behavior further lowers the service providers capacity investment and lengthens the customers duration of stay

Energy dependent kinetic freeze-out temperature and transverse flow velocity in high energy collisions

Transverse momentum spectra of negative and positive pions produced at mid-(pseudo)rapidity in inelastic or non-single-diffractive proton-proton collisions and in central nucleus-nucleus collisions over an energy range from a few GeV to above 10 TeV are analyzed by a (two-component) blast-wave model with Boltzmann-Gibbs statistics and with Tsallis statistics respectively. The model results are in similarly well agreement with the experimental data measured by a few productive collaborations who work at the Heavy Ion Synchrotron (SIS), Super Proton Synchrotron (SPS), Relativistic Heavy Ion Collider (RHIC), and Large Hadron Collider (LHC), respectively. The energy dependent kinetic freeze-out temperature and transverse flow velocity are obtained and analyzed. Both the quantities have quick increase from the SIS to SPS, and slight increase or approximate invariability from the top RHIC to LHC. Around the energy bridge from the SPS to RHIC, the considered quantities in proton-proton collisions obtained by the blast-wave model with Boltzmann-Gibbs statistics show more complex energy dependent behavior comparing with the results in other three cases.Comment: 16 pages, 4 figures. The European Physical Journal A, accepted. arXiv admin note: text overlap with arXiv:1805.0334