A note on the waiting time in M[X]/G/1 queueing systems with a removable server

2004 ◽  
Vol 41 (01) ◽  
pp. 287-291
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Waiting Time ◽  
Queueing Systems ◽  
Stieltjes Transform ◽  
Steady State Distribution ◽  
State Distribution ◽  
Removable Server ◽  
Inactive Phase ◽  
Bulk Arrival

For the M[X]/G/1 queueing model with a general exhaustive-service vacation policy, it has been proved that the Laplace-Stieltjes transform (LST) of the steady-state distribution function of the waiting time of a customer arriving while the server is active is the product of the corresponding LST in the bulk arrival model with unremovable server and another LST. The expression given for the latter, however, is valid only under the assumption that the number of groups arriving in an inactive phase is independent of the sizes of the groups. We here give an expression which holds in the general case. For the N-policy case, we also give an expression for the LST of the steady-state distribution function of the waiting time of a customer arriving while the server is inactive.

A note on the waiting time in M[X]/G/1 queueing systems with a removable server

2004 ◽  
Vol 41 (1) ◽  
pp. 287-291
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Waiting Time ◽  
Queueing Systems ◽  
Stieltjes Transform ◽  
Steady State Distribution ◽  
State Distribution ◽  
Removable Server ◽  
Inactive Phase ◽  
Bulk Arrival

For the M[X]/G/1 queueing model with a general exhaustive-service vacation policy, it has been proved that the Laplace-Stieltjes transform (LST) of the steady-state distribution function of the waiting time of a customer arriving while the server is active is the product of the corresponding LST in the bulk arrival model with unremovable server and another LST. The expression given for the latter, however, is valid only under the assumption that the number of groups arriving in an inactive phase is independent of the sizes of the groups. We here give an expression which holds in the general case. For the N-policy case, we also give an expression for the LST of the steady-state distribution function of the waiting time of a customer arriving while the server is inactive.

Slowly propagating instabilities in plasmas with Margenau-Davydov electron distribution function

1980 ◽  
Vol 24 (3) ◽  
pp. 503-514 ◽  
Author(s):  
V. J. Žigman ◽  
B. S. Milić
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Absolute Stability ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Electron Drift ◽  
Steady State Distribution ◽  
State Distribution ◽  
Weakly Ionized ◽  
Weakly Ionized Plasma

The properties of certain wave modes excited in a weakly ionized plasma placed in an external d.c. electric field are analyzed from the standpoint of the linearized kinetic equation, the electron steady-state distribution function being taken in the form of the extended Margenau–Davydov and, in particular, Druyvesteinian. The presence of absolute stability cones formed by certain propagation directions is found. The corresponding critical values of the electron drift, destabilizing each of the modes considered, is also evaluated for a plasma with a Druyvesteinian distribution.

A NEW LOOK AT ORGAN TRANSPLANTATION MODELS AND DOUBLE MATCHING QUEUES

2011 ◽  
Vol 25 (2) ◽  
pp. 135-155 ◽  
Author(s):  
Onno J. Boxma ◽  
Israel David ◽  
David Perry ◽  
Wolfgang Stadje
Keyword(s):  
Steady State ◽  
Organ Transplantation ◽  
Waiting Time ◽  
Queueing Theory ◽  
Waiting Lists ◽  
Performance Criteria ◽  
Prototype Model ◽  
Steady State Distribution ◽  
State Distribution ◽  
Long Run

In this paper we propose a prototype model for the problem of managing waiting lists for organ transplantations. Our model captures the double-queue nature of the problem: there is a queue of patients, but also a queue of organs. Both may suffer from “impatience”: the health of a patient may deteriorate, and organs cannot be preserved longer than a certain amount of time. Using advanced tools from queueing theory, we derive explicit results for key performance criteria: the rate of unsatisfied demands and of organ outdatings, the steady-state distribution of the number of organs on the shelf, the waiting time of a patient, and the long-run fraction of time during which the shelf is empty of organs.

On a decomposition result for a class of vacation queueing systems

1990 ◽  
Vol 27 (1) ◽  
pp. 227-231 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Steady State ◽  
Time Distribution ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
State Distribution ◽  
Random Size ◽  
Poisson Arrivals ◽  
General Service

We consider a single-server infinite-capacity queueing sysem with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distribution of the actual waiting time of a customer arriving while the server is active.

The Diffusion and Thermalization of an Electron Cloud Injected into an Afterglow Plasma

1971 ◽  
Vol 49 (9) ◽  
pp. 1124-1136
Author(s):  
H. W. H. Van Andel
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Steady State ◽  
Boltzmann Equation ◽  
Axial Magnetic Field ◽  
Electron Cloud ◽  
Steady State Distribution ◽  
State Distribution ◽  
Account Electron ◽  
Afterglow Plasma

The steady state distribution function for a suprathermal electron cloud injected into a cylindrical plasma is found as a function of position and velocity by solving the Boltzmann equation numerically in the Fokker–Planck approximation with an added term taking into account electron-neutral collisions. The injection is assumed to take place at one end of the cylinder, and an axial magnetic field is assumed present. A number of representative solutions are given for various choices of the parameters of the problem.

scholarly journals Tail Asymptotics for a Random Sign Lindley Recursion

2010 ◽  
Vol 47 (1) ◽  
pp. 72-83 ◽  
Author(s):  
Maria Vlasiou ◽  
Zbigniew Palmowski
Keyword(s):  
Steady State ◽  
Storage Systems ◽  
Queueing Systems ◽  
Service Systems ◽  
Tail Asymptotics ◽  
Steady State Distribution ◽  
State Distribution ◽  
Random Sign ◽  
Special Cases ◽  
Tail Behaviour

We investigate the tail behaviour of the steady-state distribution of a stochastic recursion that generalises Lindley's recursion. This recursion arises in queueing systems with dependent interarrival and service times, and includes alternating service systems and carousel storage systems as special cases. We obtain precise tail asymptotics in three qualitatively different cases, and compare these with existing results for Lindley's recursion and for alternating service systems.

The effects of thermal motion of neutrals on the non-potential instabilities in a weakly ionized sodium plasma

1982 ◽  
Vol 28 (1) ◽  
pp. 177-184 ◽  
Author(s):  
V. J. Žigman ◽  
B. S. Milić
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Cross Section ◽  
Thermal Motion ◽  
Moderate Intensity ◽  
Experimental Measurements ◽  
Steady State Distribution ◽  
State Distribution ◽  
Weakly Ionized ◽  
Sodium Plasma

The results of recent experimental measurements of the differential cross-section for elastic scattering of electrons on sodium atoms were used to evaluate the electron steady-state distribution function in a weakly ionized, uniform and non-magnetized sodium plasma placed in a d.c. electric field. The field was assumed to be of moderate intensity, so that the thermal motion of the neutrals had to be taken into account in the evaluation of the distribution function. The resulting ‘modified Druyvesteinian function’ was applied to study the non-potential instabilities arising from the presence of the field in this particular plasma. Threshold drifts for both very slow and slow modes were obtained and the conditions for the onset of instabilities were discussed. It is shown that the thermal motion of the neutrals affects both critical drifts and the angles of propagation.

On a decomposition result for a class of vacation queueing systems

1990 ◽  
Vol 27 (01) ◽  
pp. 227-231 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Steady State ◽  
Time Distribution ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
State Distribution ◽  
Random Size ◽  
Poisson Arrivals ◽  
General Service

We consider a single-server infinite-capacity queueing sysem with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distribution of the actual waiting time of a customer arriving while the server is active.

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