The double-ended queue with social and economic situations

AUTHOR AND
AFFILIATION

1RAM KHILAWAN TIWARI and 2DHARMENDRA BADAL
1Department of Mathematics G.B.S College Mauranipur India

2Department of Mathematical Sciences and Computer Applications Bundelkhand University Jhansi UP India

KEYWORDS:

Double ended queue, limited waiting space, socialsituations.

Issue Date:

1RAM KHILAWAN TIWARI and 2DHARMENDRA BADAL, “The double-ended queue with social and economic situations”, Journal of Ultra Scientist of Physical Sciences, Volume 24, Issue 3, Page Number , 2016

Pages:

1RAM KHILAWAN TIWARI and 2DHARMENDRA BADAL, “The double-ended queue with social and economic situations”, Journal of Ultra Scientist of Physical Sciences, Volume 24, Issue 3, Page Number , 2016

Available from: http://www.ultrascientist.org/paper/540/

ISSN:

2319-8044 (Online) – 2231-346X (Print)

Source:

PDF

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DOI:

jusps-A

ABSTRACT:

The double-ended queue involving trains and passangers at a Railway station has been considered under the assumption that there is limited waiting space both for trains and for passangers. The arrival distribution of trains is simulated by means of an arrival timing channel consisting of j phases. The arrivals of passangers are assumed to be Poisson distributed. In the time dependent case we obtain an expression for the Laplace transform of the probabilities that there are n units in the queue. The cases of exponential and 2-Erlang arrival distributions for trains have been considered as particular cases. In the steady state, for a 2-Erlang arrival distribution for trains, we have evaluated the probabilities that the waiting space for passangers or trains is full in different particular cases. Their values are also shown by means of graphs.

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The double-ended queue involving trains and passangers at a Railway station has been considered under the assumption that there is limited waiting space both for trains and for passangers. The arrival distribution of trains is simulated by means of an arrival timing channel consisting of j phases. The arrivals of passangers are assumed to be Poisson distributed. In the time dependent case we obtain an expression for the Laplace transform of the probabilities that there are n units in the queue. The cases of exponential and 2-Erlang arrival distributions for trains have been considered as particular cases. In the steady state, for a 2-Erlang arrival distribution for trains, we have evaluated the probabilities that the waiting space for passangers or trains is full in different particular cases. Their values are also shown by means of graphs.