On infinite server queues with batch arrivals

1966 ◽  
Vol 3 (1) ◽  
pp. 274-279 ◽  
Author(s):  
D. N. Shanbhag

The queueing system studied in this paper is the one in which (i)there are an infinite number of servers,(ii)initially (at t = 0) all the servers are idle,(iii)one server serves only one customer at a time and the service times are independent and identically distributed with distribution function B(t) (t > 0) and mean β(< ∞),(iv)the arrivals are in batches such that a batch arrives during (t, t + δt) with probability λ(t)δt + o(δt) (λ(t) > 0) and no arrival takes place during (t, t + δt) with the probability 1 –λ(t)δt + o(δt),(v)the batch sizes are independent and identically distributed with mean α(< ∞), and the probability that a batch size equals r is given by ar(r ≧ 1),(vi)the batch sizes, the service times and the arrivals are independent.

1966 ◽  
Vol 3 (01) ◽  
pp. 274-279 ◽  
Author(s):  
D. N. Shanbhag

The queueing system studied in this paper is the one in which (i) there are an infinite number of servers, (ii) initially (at t = 0) all the servers are idle, (iii) one server serves only one customer at a time and the service times are independent and identically distributed with distribution function B(t) (t &gt; 0) and mean β(&lt; ∞), (iv) the arrivals are in batches such that a batch arrives during (t, t + δt) with probability λ(t)δt + o(δt) (λ(t) &gt; 0) and no arrival takes place during (t, t + δt) with the probability 1 –λ(t)δt + o(δt), (v) the batch sizes are independent and identically distributed with mean α(&lt; ∞), and the probability that a batch size equals r is given by a r(r ≧ 1), (vi) the batch sizes, the service times and the arrivals are independent.


1969 ◽  
Vol 6 (1) ◽  
pp. 154-161 ◽  
Author(s):  
E.G. Enns

In the study of the busy period for a single server queueing system, three variables that have been investigated individually or at most in pairs are:1.The duration of the busy period.2.The number of customers served during the busy period.3.The maximum number of customers in the queue during the busy period.


1971 ◽  
Vol 8 (04) ◽  
pp. 828-834 ◽  
Author(s):  
Asha Seth Kapadia

Kingman (1962) studied the effect of queue discipline on the mean and variance of the waiting time. He made no assumptions regarding the stochastic nature of the input and the service distributions, except that the input and service processes are independent of each other. When the following two conditions hold: (a) no server sits idle while there are customers waiting to be served; (b) the busy period is finite with probability one (i.e., the queue empties infinitely often with probability one); he has shown that the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in order of their arrival. Conditions (a) and (b) will henceforward be called Kingman conditions and a queueing system satisfying Kingman conditions will be referred to in the text as a Kingman queue.


1989 ◽  
Vol 134 ◽  
pp. 406-407
Author(s):  
J. P. Vader ◽  
J. A. Frogel ◽  
F. C. Gillett ◽  
M. H. K. de Grijp

The IRAS Point Source Catalog contains only 61 sources identified as galaxies whose energy distribution peaks at 60 mμ. The scarcity of such galaxies has prompted a search for possible common properties. This sample of ‘60 mμ peakers’, 21 of which are previously identified galaxies, partially overlaps with that of warm IRAS galaxies studied by de Grijp et al. (1987) and contains similar percentages of Seyfert (65%) and starburst galaxies on the one hand, and of strong and weak radio sources on the other hand. A remarkable characteristic is, however, that about half of the 60 mμ peakers seem to be early-type galaxies. The fact that such galaxies are rarely IRAS sources and, if so, have FIR energy distributions peaking at 100 mμ similar to those of spirals, implies that we are sampling active or nuclear starburst early-type galaxies with a very large success rate. The observational data accumulated so far further show that: (i)objects with smaller FIR to near-IR flux ratios have redder J-K colors and warmer 60 to 25 mμ colors, i.e., an infared spectrum dominated by warmer dust and/or a nonthermal source (Figs. 1a,b);(ii)out of 32 objects with radio data, the 5 compact radio sources with luminosities intermediate between those af radio-quiet and radio-loud AGN have among the warmest 60 to 25 mμ colors (Fig. 2). Such warm FIR colors are not a common characteristic of radio galaxies and quasars (Golombek et al. 1987, Neugebauer et al. 1986).(iii)the 60 mμ luminosities range from 109 to 1012 L0, and are largest for Mkn 231, 2306+0505 (Hill et al. 1987) and 2046+1925 (Frogel et al. 1988). The latter 2 objects, along with 0052-7054 (Frogel and Elias 1987) which also belongs to our sample, are Seyfert 2 galaxies with evidence for the presence of a dust-obsured broad line region.


Author(s):  
Yosuke Sato
Keyword(s):  
The One ◽  

Merchant (2004) proposes that a fragmentary response like the one in (1b) to the question in (1a) is derived from its full-fledged sentential counterpart in (1c).(1) a.Who did she see?b.[DP John]c.[TPShe saw John] (Merchant 2004:673)


1939 ◽  
Vol 12 (1-2) ◽  
pp. 27-55

The connection between the Colour of the Eyes, the Mortality, and the Production of White Leghorns. Het Verband tusschen de oogkleur van Witte Leghorns en de Herfte en de productie. Dr. J. B. van der Meulen. Landbouwkundig Tijdschrift, Vol. 50, 1938, p. 868.An investigation, in which 406 White Leghorns of two different strains were used, on the connection between the colour of the eyes of normal healthy pullets at the beginning of the laying period on the one hand and the production and mortality during the pullet year on the other hand, led to the following conclusions:—1.The mortality amongst hens with abnormal colour of the eyes, (brown-grey and/or blue) is considerably higher than that amongst birds with normal orange coloured eyes, and the production of the former is on the average lower than that of the latter.2.Birds with one normal and one abnormal coloured eyes, correspond to birds with normal coloured eyes as far as mortality is concerned, but their average production resembles more than that of birds with two abnormal eyes.3.Not only an abnormal eye colour but also an abnormal shape of the pupil seems to point to higher mortality and the highest mortality is probable amongst birds which have both an abnormal colour, as well as an abnormal shape of the pupil.


1986 ◽  
Vol 109 ◽  
pp. 19-42 ◽  
Author(s):  
V. A. Brumberg

The nonuniqueness of the quasi-Galilean coordinates of general relativity leads to the emergence of unmeasurable coordinate-dependent quantities in astronomical practice. One may offer three possible ways to overcome the related difficulties: 1.developing theoretical conclusions only in terms of measurable quantities2.using arbitrary coordinates and developing an unambiguous procedure for comparing measurable and calculated quantities3.agreement to utilize one and only one coordinate system.In this paper we prefer the second way. After formulating the heliocentric planetary and geocentric satellite equations of motion, the general technique for relativistic reduction in astrometry and geodynamics is developed. Specific algorithms for the reduction of absolute and relative measurements are derived for the one- and the two- body problem. For illustration, the relativistic reduction of stellar parallaxes, Doppler satellite observations, navigation measurements with the aid of satellites and radiointerferometric measurements are presented in detail.


1971 ◽  
Vol 8 (4) ◽  
pp. 828-834 ◽  
Author(s):  
Asha Seth Kapadia

Kingman (1962) studied the effect of queue discipline on the mean and variance of the waiting time. He made no assumptions regarding the stochastic nature of the input and the service distributions, except that the input and service processes are independent of each other. When the following two conditions hold: (a)no server sits idle while there are customers waiting to be served;(b)the busy period is finite with probability one (i.e., the queue empties infinitely often with probability one); he has shown that the mean waiting time is independent of the queue discipline and the variance of the waiting time is a minimum when the customers are served in order of their arrival. Conditions (a) and (b) will henceforward be called Kingman conditions and a queueing system satisfying Kingman conditions will be referred to in the text as a Kingman queue.


1969 ◽  
Vol 6 (01) ◽  
pp. 154-161 ◽  
Author(s):  
E.G. Enns

In the study of the busy period for a single server queueing system, three variables that have been investigated individually or at most in pairs are: 1. The duration of the busy period. 2. The number of customers served during the busy period. 3. The maximum number of customers in the queue during the busy period.


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