A note on joining strategies for two queues in parallel

OPSEARCH ◽  
2008 ◽  
Vol 45 (2) ◽  
pp. 111-118
Author(s):  
S. N. Singh ◽  
Rekha Tiwari
Keyword(s):  
Queues In Parallel

A note on waiting times in systems with queues in parallel

1987 ◽  
Vol 24 (2) ◽  
pp. 540-546 ◽  
Author(s):  
J. P. C. Blanc
Keyword(s):  
Queue Length ◽  
Time Distribution ◽  
Waiting Times ◽  
Numerical Data ◽  
Series Expansions ◽  
Waiting Time Distribution ◽  
Power Series Expansions ◽  
The Mean ◽  
Waiting Line ◽  
Queues In Parallel

Numerical data are presented concerning the mean and the standard deviation of the waiting-time distribution for multiserver systems with queues in parallel, in which customers choose one of the shortest queues upon arrival. Moreover, a new numerical method is outlined for calculating state probabilities and moments of queue-length distributions. This method is based on power series expansions and recursion. It is applicable to many systems with more than one waiting line.

The autostrada queueing problem

1984 ◽  
Vol 21 (2) ◽  
pp. 394-403 ◽  
Author(s):  
B. W. Conolly
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Waiting Room ◽  
Queue System ◽  
Room Size ◽  
Fresh Perspective ◽  
Queues In Parallel

The model considered in this note has been referred to by Haight (1958), Kingman (1961) and Flatto and McKean (1977) as two queues in parallel. Customers choose the shorter of the two queues which are otherwise independent. This system is known to be inferior to a single queue feeding the two servers, but how much? Some elementary considerations provide a fresh perspective on this awkward boundary-value problem. A procedure is proposed for the solution in the context of finite waiting-room size and some comparisons are made with the single-queue system and an independent two-queue system.

On Two Queues in Parallel

Biometrika ◽  
1960 ◽  
Vol 47 (1/2) ◽  
pp. 198 ◽  
Author(s):  
Coleridge A. Wilkins
Keyword(s):  
Queues In Parallel

Parallel fluid queues with constant inflows and simultaneous random reductions

2001 ◽  
Vol 38 (3) ◽  
pp. 609-620 ◽  
Author(s):  
Offer Kella ◽  
Masakiyo Miyazawa
Keyword(s):  
Poisson Process ◽  
Upper Bounds ◽  
Decay Rates ◽  
Fluid Queue ◽  
Linear Combinations ◽  
Fluid Queues ◽  
Constant Rate ◽  
Major Interest ◽  
Dimensional Distribution ◽  
Queues In Parallel

We consider I fluid queues in parallel. Each fluid queue has a deterministic inflow with a constant rate. At a random instant subject to a Poisson process, random amounts of fluids are simultaneously reduced. The requested amounts for the reduction are subject to a general I-dimensional distribution. The queues with inventories that are smaller than the requests are emptied. Stochastic upper bounds are considered for the stationary distribution of the joint buffer contents. Our major interest is in finding exponential product-form bounds, which turn out to have the appropriate decay rates with respect to certain linear combinations of buffer contents.

The autostrada queueing problem

1984 ◽  
Vol 21 (02) ◽  
pp. 394-403 ◽  
Author(s):  
B. W. Conolly
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Waiting Room ◽  
Queue System ◽  
Room Size ◽  
Fresh Perspective ◽  
Queues In Parallel

The model considered in this note has been referred to by Haight (1958), Kingman (1961) and Flatto and McKean (1977) as two queues in parallel. Customers choose the shorter of the two queues which are otherwise independent. This system is known to be inferior to a single queue feeding the two servers, but how much? Some elementary considerations provide a fresh perspective on this awkward boundary-value problem. A procedure is proposed for the solution in the context of finite waiting-room size and some comparisons are made with the single-queue system and an independent two-queue system.

TWO QUEUES IN PARALLEL

Biometrika ◽  
1958 ◽  
Vol 45 (3-4) ◽  
pp. 401-410 ◽  
Author(s):  
FRANK A. HAIGHT
Keyword(s):  
Queues In Parallel

The shortest queue problem

1985 ◽  
Vol 22 (4) ◽  
pp. 865-878 ◽  
Author(s):  
Shlomo Halfin
Keyword(s):  
Linear Programming ◽  
Heavy Traffic ◽  
Single Server ◽  
Service Center ◽  
Poisson Stream ◽  
Programming Techniques ◽  
Shortest Queue ◽  
Number Of Customers ◽  
Queues In Parallel ◽  
Shortest Queue Problem

A Poisson stream of customers arrives at a service center which consists of two single-server queues in parallel. The service times of the customers are exponentially distributed, and both servers serve at the same rate. Arriving customers join the shortest of the two queues, with ties broken in any plausible manner. No jockeying between the queues is allowed. Employing linear programming techniques, we calculate bounds for the probability distribution of the number of customers in the system, and its expected value in equilibrium. The bounds are asymptotically tight in heavy traffic.

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