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

Approximation of Rectangular Beta-Laguerre Ensembles and Large Deviations

We investigate the random eigenvalues coming from the beta-Laguerre ensemble with parameter p, which is a generalization of the real, complex and quaternion Wishart matrices of parameter (n,p). In the case that the sample size n is much smaller than the dimension of the population distribution p, a common situation in modern data, we approximate the beta-Laguerre ensemble by a beta-Hermite ensemble which is a generalization of the real, complex and quaternion Wigner matrices. As corollaries, when n is much smaller than p, we show that the largest and smallest eigenvalues of the complex Wishart matrix are asymptotically independent; we obtain the limiting distribution of the condition numbers as a sum of two i.i.d. random variables with a Tracy-Widom distribution, which is much different from the exact square case that n=p by Edelman (1988); we propose a test procedure for a spherical hypothesis test. By the same approximation tool, we obtain the asymptotic distribution of the smallest eigenvalue of the beta-Laguerre ensemble. In the second part of the paper, under the assumption that n is much smaller than p in a certain scale, we prove the large deviation principles for three basic statistics: the largest eigenvalue, the smallest eigenvalue and the empirical distribution of eigenvalues, where the last large deviation is derived by using a non-standard method

Implementation and Investigation of a Compact Circular Wide Slot UWB Antenna with Dual Notched Band Characteristics using Stepped Impedance Resonators

A coplanar waveguide (CPW) fed ultra-wideband (UWB) antenna with dual notched band characteristics is presented in this paper. The circular wide slot and circular radiation patch are utilized to broaden the impedance bandwidth of the UWB antenna. The dual notched band functions are achieved by employing two stepped impedance resonators (SIRs) which etched on the circular radiation patch and CPW excitation line, respectively. The two notched bands can be controlled by adjusting the dimensions of the two stepped impedance resonators which give tunable notched band functions. The proposed dual notched band UWB antenna has been designed in details and optimized by means of HFSS. Experimental and numerical results show that the proposed antenna with compact size of 32 × 24 mm2, has an impedance bandwidth range from 2.8 GHz to 13.5 Hz for voltage standing-wave ratio (VSWR) less than 2, except the notch bands 5.0 GHz - 6.2 GHz for HIPERLAN/2 and IEEE 802.11a (5.1 GHz - 5.9 GHz) and 8.0 GHz - 9.3 GHz for satellite and military applications