scholarly journals Tail Asymptotics for the Queue Size Distribution in an M/G/1 Retrial Queue

2007 ◽  
Vol 44 (04) ◽  
pp. 1111-1118 ◽  
Author(s):  
Jerim Kim ◽  
Bara Kim ◽  
Sung-Seok Ko
Keyword(s):  
Size Distribution ◽  
Service Time ◽  
Generating Functions ◽  
Time Distribution ◽  
Retrial Queue ◽  
Service Time Distribution ◽  
Tail Asymptotics ◽  
Queue Size ◽  
Exponential Moment ◽  
Geometric Function

We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.

scholarly journals Tail Asymptotics for the Queue Size Distribution in an M/G/1 Retrial Queue

2007 ◽  
Vol 44 (4) ◽  
pp. 1111-1118 ◽  
Author(s):  
Jerim Kim ◽  
Bara Kim ◽  
Sung-Seok Ko
Keyword(s):  
Size Distribution ◽  
Service Time ◽  
Generating Functions ◽  
Time Distribution ◽  
Retrial Queue ◽  
Service Time Distribution ◽  
Tail Asymptotics ◽  
Queue Size ◽  
Exponential Moment ◽  
Geometric Function

We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.

Tail asymptotics for the queue size distribution in the MAP/G/1 retrial queue

2010 ◽  
Vol 66 (1) ◽  
pp. 79-94 ◽  
Author(s):  
Bara Kim ◽  
Jeongsim Kim ◽  
Jerim Kim
Keyword(s):  
Size Distribution ◽  
Retrial Queue ◽  
Tail Asymptotics ◽  
Queue Size

Hitting time in an M/G/1 queue

1999 ◽  
Vol 36 (03) ◽  
pp. 934-940 ◽  
Author(s):  
Sheldon M. Ross ◽  
Sridhar Seshadri
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
Arrival Rate ◽  
Hitting Time ◽  
Service Time Distribution ◽  
Expected Time ◽  
Efficient Simulation ◽  
Simulation Procedure ◽  
Poisson Arrival ◽  
Stationary Delay

We study the expected time for the work in an M/G/1 system to exceed the level x, given that it started out initially empty, and show that it can be expressed solely in terms of the Poisson arrival rate, the service time distribution and the stationary delay distribution of the M/G/1 system. We use this result to construct an efficient simulation procedure.

The general bulk queue as a matrix factorisation problem of the Wiener-Hopf type. Part II.

1975 ◽  
Vol 7 (3) ◽  
pp. 647-655 ◽  
Author(s):  
John Dagsvik
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Time Process ◽  
Waiting Time Process ◽  
Bulk Queue ◽  
Erlang Distributions ◽  
Matrix Factorisation

In a previous paper (Dagsvik (1975)) the waiting time process of the single server bulk queue is considered and a corresponding waiting time equation is established. In this paper the waiting time equation is solved when the inter-arrival or service time distribution is a linear combination of Erlang distributions. The analysis is essentially based on algebraic arguments.

An extension of Erlang's formulas which distinguishes individual servers

1972 ◽  
Vol 9 (1) ◽  
pp. 192-197 ◽  
Author(s):  
Jan M. Chaiken ◽  
Edward Ignall
Keyword(s):  
Service Time ◽  
Time Distribution ◽  
The State ◽  
Service Time Distribution ◽  
Loss System ◽  
Arbitrary Service Time

For a particular kind of finite-server loss system in which the number and identity of servers depends on the type of the arriving call and on the state of the system, the limits of the state probabilities (as t → ∞) are found for an arbitrary service-time distribution.

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