Diffusion Models for Double-ended Queues with Renewal Arrival Processes

We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers simultaneously in the system. We assume that sellers and buyers arrive at the system according to independent renewal processes, and they would leave the system after independent exponential patience times. We establish fluid and diffusion approximations for the queue length process under a suitable asymptotic regime. The fluid limit is the solution of an ordinary differential equation, and the diffusion limit is a time-inhomogeneous asymmetric Ornstein-Uhlenbeck process (O-U process). A heavy traffic analysis is also developed, and the diffusion limit in the stronger heavy traffic regime is a time-homogeneous asymmetric O-U process. The limiting distributions of both diffusion limits are obtained. We also show the interchange of the heavy traffic and steady state limits

Associated HI absorption in the z=3.4 radio galaxy B2 0902+343 observed with the GMRT

We have made observations of the associated HI absorption of a high redshift radio galaxy 0902+34 at z=3.395 with the Giant Meterwave Radio Telescope in the $323\pm1$ MHz band. We find a narrow absorption line with a flux density of 11.5 mJy at a redshift of 3.397 consistent with that observed by Uson et al. (1991), Briggs et al. (1993) and de Bruyn (1996).A weak broad absorption feature reported by de Bruyn (1996) has not been detected in our observations. We also place an upper limit of 4 mJy (2 $\sigma$) on emission line strength at the position where Uson et al. (1991) claimed to have found a narrow emission line.Comment: To appear in Journal of Astronomy and Astrophysic

Pruning the Lyman alpha forest of Q1331+170

A multitude of absorption lines seen shortward of QSO Ly-alpha emission, that cannot be traced to heavy element absorption systems, are assumed to be Ly-alpha lines arising in intervening clouds. Studies of these Ly-alpha clouds, typically done at 1 A or lower resolution, have shown N(H1) approximately equal to 10(exp 13) - 10(exp 17) sq cm and b approximately equal to 35 km/s. Sargent et al 1980, on the basis of a flat pair velocity correlation function (PVCF), argued that these clouds are intergalactic. But Crotts 1989 showed that the strong Ly-alpha lines are spatially clustered. High resolution studies of Webb 1987 and Rauch et al 1992 also report some evidence for weak clustering, but overall such high resolution studies have been rare. A study of the Ly-alpha forest of Q1331 + 170 over x(sub abs) = 1.60 - 2.19 based on 18 km/s resolution data at S/N approximately equal to 15, with metal-line deblending incorporated