In this paper we consider nonhomogeneous birth and death processes (BDP) with periodic rates. Two important parameters are studied, which are helpful to describe a nonhomogeneous BDP X = X (t), t ≥ 0: the limiting mean value (namely, the mean length of the queue at a given time t) and the double mean (i.e. the mean length of the queue for the whole duration of the BDP). We find conditions of existence of the means and determine bounds for their values, involving also the truncated BDP X N . Finally we present some examples where these bounds are used in order to approximate the double mean.

Pollen records from perennially frozen sequences provide vegetation and climate reconstruction for the last 48,000 14C years in the central part of Taymyr Peninsula. Open larch forest with Alnus fruticosa and Betula nana grew during the Kargin (Middle Weichselian) Interstade, ca. 48,000–25,000 14C yr B.P. The climate was generally warmer and wetter than today. Open steppe-like communities with Artemisia, Poaceae, Asteraceae, and herb tundralike communities with dwarf Betula and Salix dominated during the Sartan (Late Weichselian) Stade, ca. 24,000–10,300 14C yr B.P. The statistical information method used for climate reconstruction shows that the coldest climate was ca. 20,000–17,000 14C yr B.P. A warming (Allerød Interstade?) with mean July temperature ca. 1.5°C warmer than today occurred ca. 12,000 14C yr B.P. The following cooling with temperatures about 3°–4°C cooler than present and precipitation about 100 mm lower corresponds well with the Younger Dryas Stade. Tundra–steppe vegetation changed to Betula nana–Alnus fruticosa shrub tundra ca. 10,000 14C yr B.P. Larch appeared in the area ca. 9400 14C yr B.P. and disappeared after 2900 14C yr B.P. Cooling events ca. 10,500, 9600, and 8200 14C yr B.P. characterized the first half of the Holocene. A significant warming occurred ca. 8500 14C yr B.P., but the Holocene temperature maximum was at about 6000–4500 14C yr B.P. The vegetation cover approximated modern conditions ca. 2800 14C yr B.P. Late Holocene warming events occurred at ca. 3500, 2000, and 1000 14C yr B.P. A cooling (Little Ice Age?) took place between 500 and 200 14C yr ago.

No abstract

We consider M t /M t /S-type queueing model with group services. Bounds on the rate of convergence for the queue-length process are obtained. Ordinary M t /M t /S queue and M t /M t /S type queueing model with group services are studied as examples.

No abstract