The M/G/1 queue with negative customers

1996 ◽  
Vol 28 (02) ◽  
pp. 540-566 ◽  
Author(s):  
Peter G. Harrison ◽  
Edwige Pitel
Keyword(s):  
Iterative Solution ◽  
Single Server ◽  
Negative Customers ◽  
Poisson Arrival ◽  
First Case ◽  
Full Study ◽  
Service Times ◽  
The Stability ◽  
The One ◽  
Iterative Solution Method

We derive expressions for the generating function of the equilibrium queue length probability distribution in a single server queue with general service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. For the case of first come first served queueing discipline for the positive customers, we compare the killing strategies in which either the last customer in the queue or the one in service is removed by a negative customer. We then consider preemptive-restart with resampling last come first served queueing discipline for the positive customers, combined with the elimination of the customer in service by a negative customer—the case of elimination of the last customer yields an analysis similar to first come first served discipline for positive customers. The results show different generating functions in contrast to the case where service times are exponentially distributed. This is also reflected in the stability conditions. Incidently, this leads to a full study of the preemptive-restart with resampling last come first served case without negative customers. Finally, approaches to solving the Fredholm integral equation of the first kind which arises, for instance, in the first case are considered as well as an alternative iterative solution method.

The M/G/1 queue with negative customers

1996 ◽  
Vol 28 (2) ◽  
pp. 540-566 ◽  
Author(s):  
Peter G. Harrison ◽  
Edwige Pitel
Keyword(s):  
Iterative Solution ◽  
Single Server ◽  
Negative Customers ◽  
Poisson Arrival ◽  
First Case ◽  
Full Study ◽  
Service Times ◽  
The Stability ◽  
The One ◽  
Iterative Solution Method

We derive expressions for the generating function of the equilibrium queue length probability distribution in a single server queue with general service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. For the case of first come first served queueing discipline for the positive customers, we compare the killing strategies in which either the last customer in the queue or the one in service is removed by a negative customer. We then consider preemptive-restart with resampling last come first served queueing discipline for the positive customers, combined with the elimination of the customer in service by a negative customer—the case of elimination of the last customer yields an analysis similar to first come first served discipline for positive customers. The results show different generating functions in contrast to the case where service times are exponentially distributed. This is also reflected in the stability conditions. Incidently, this leads to a full study of the preemptive-restart with resampling last come first served case without negative customers. Finally, approaches to solving the Fredholm integral equation of the first kind which arises, for instance, in the first case are considered as well as an alternative iterative solution method.

Sojourn times in single-server queues by negative customers

1993 ◽  
Vol 30 (4) ◽  
pp. 943-963 ◽  
Author(s):  
P. G. Harrison ◽  
E. Pitel
Keyword(s):  
Laplace Transform ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Negative Customers ◽  
Mean Values ◽  
Poisson Arrival ◽  
Server Queue ◽  
The Laplace Transform ◽  
Time Density

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.

scholarly journals Stability of retrial queues with versatile retrial policy

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Tewfik Kernane ◽  
Amar Aïssani
Keyword(s):  
Poisson Process ◽  
Strong Coupling ◽  
Sufficient Conditions ◽  
Retrial Queues ◽  
Negative Customers ◽  
Batch Arrivals ◽  
Unreliable Server ◽  
Service Times ◽  
The Stability

We consider in this paper the stability of retrial queues with a versatile retrial policy. We obtain sufficient conditions for the stability by the strong coupling convergence to a stationary ergodic regime for various models of retrial queues including a model with two types of customers, a model with breakdowns of the server, a model with negative customers, and a model with batch arrivals. For all the models considered we assume that the service times are general stationary ergodic and interarrival and retrial times are i.i.d. sequences exponentially distributed. For the model with unreliable server we also assume that the repair times are stationary and ergodic and the occurrences of breakdowns follow a Poisson process.

Queues with negative arrivals

1991 ◽  
Vol 28 (1) ◽  
pp. 245-250 ◽  
Author(s):  
Erol Gelenbe ◽  
Peter Glynn ◽  
Karl Sigman
Keyword(s):  
Stability Conditions ◽  
Queueing Models ◽  
Single Server ◽  
New Models ◽  
Service Rates ◽  
Service Times ◽  
The Stability ◽  
Negative Arrivals ◽  
The Way

We study single-server queueing models where in addition to regular arriving customers, there are negative arrivals. A negative arrival has the effect of removing a customer from the queue. The way in which this removal is specified gives rise to several different models. Unlike the standard FIFOGI/GI/1 model, the stability conditions for these new models may depend upon more than just the arrival and service rates; the entire distributions of interarrival and service times may be involved.

Sojourn times in single-server queues by negative customers

1993 ◽  
Vol 30 (04) ◽  
pp. 943-963
Author(s):  
P. G. Harrison ◽  
E. Pitel
Keyword(s):  
Laplace Transform ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Negative Customers ◽  
Mean Values ◽  
Poisson Arrival ◽  
Server Queue ◽  
The Laplace Transform ◽  
Time Density

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.

Queues with negative arrivals

1991 ◽  
Vol 28 (01) ◽  
pp. 245-250 ◽  
Author(s):  
Erol Gelenbe ◽  
Peter Glynn ◽  
Karl Sigman
Keyword(s):  
Stability Conditions ◽  
Queueing Models ◽  
Single Server ◽  
New Models ◽  
Service Rates ◽  
Service Times ◽  
The Stability ◽  
Negative Arrivals ◽  
The Way

We study single-server queueing models where in addition to regular arriving customers, there are negative arrivals. A negative arrival has the effect of removing a customer from the queue. The way in which this removal is specified gives rise to several different models. Unlike the standard FIFO GI/GI/1 model, the stability conditions for these new models may depend upon more than just the arrival and service rates; the entire distributions of interarrival and service times may be involved.

Use of a Lyophilized Reference Plasma to Compare Coagulation Test Procedures

1975 ◽  
Vol 34 (02) ◽  
pp. 426-444 ◽  
Author(s):  
J Kahan ◽  
I Nohén
Keyword(s):  
Oral Anticoagulant Therapy ◽  
Repeated Measurements ◽  
Test Procedures ◽  
Coagulation Activity ◽  
Close Relationship ◽  
Measured Activity ◽  
Test Materials ◽  
The Difference ◽  
The Stability ◽  
The One

SummaryIn 4 collaborative trials, involving a varying number of hospital laboratories in the Stockholm area, the coagulation activity of different test materials was estimated with the one-stage prothrombin tests routinely used in the laboratories, viz. Normotest, Simplastin-A and Thrombotest. The test materials included different batches of a lyophilized reference plasma, deep-frozen specimens of diluted and undiluted normal plasmas, and fresh and deep-frozen specimens from patients on long-term oral anticoagulant therapy.Although a close relationship was found between different methods, Simplastin-A gave consistently lower values than Normotest, the difference being proportional to the estimated activity. The discrepancy was of about the same magnitude on all the test materials, and was probably due to a divergence between the manufacturers’ procedures used to set “normal percentage activity”, as well as to a varying ratio of measured activity to plasma concentration. The extent of discrepancy may vary with the batch-to-batch variation of thromboplastin reagents.The close agreement between results obtained on different test materials suggests that the investigated reference plasma could be used to calibrate the examined thromboplastin reagents, and to compare the degree of hypocoagulability estimated by the examined PIVKA-insensitive thromboplastin reagents.The assigned coagulation activity of different batches of the reference plasma agreed closely with experimentally obtained values. The stability of supplied batches was satisfactory as judged from the reproducibility of repeated measurements. The variability of test procedures was approximately the same on different test materials.

Structure, Stability and Water Adsorption on Ultra-Thin TiO2 Supported on TiN

2019 ◽  
Author(s):  
Jose Julio Gutierrez Moreno ◽  
Marco Fronzi ◽  
Pierre Lovera ◽  
alan O'Riordan ◽  
Mike J Ford ◽  
...  
Keyword(s):  
Density Functional ◽  
Water Adsorption ◽  
Chemical Potential ◽  
Energy Gap ◽  
Molecular Water ◽  
Structure Stability ◽  
Ambient Conditions ◽  
Rutile Structure ◽  
The Stability ◽  
The One

<p></p><p>Interfacial metal-oxide systems with ultrathin oxide layers are of high interest for their use in catalysis. In this study, we present a density functional theory (DFT) investigation of the structure of ultrathin rutile layers (one and two TiO<sub>2</sub> layers) supported on TiN and the stability of water on these interfacial structures. The rutile layers are stabilized on the TiN surface through the formation of interfacial Ti–O bonds. Charge transfer from the TiN substrate leads to the formation of reduced Ti<sup>3+</sup> cations in TiO<sub>2.</sub> The structure of the one-layer oxide slab is strongly distorted at the interface, while the thicker TiO<sub>2</sub> layer preserves the rutile structure. The energy cost for the formation of a single O vacancy in the one-layer oxide slab is only 0.5 eV with respect to the ideal interface. For the two-layer oxide slab, the introduction of several vacancies in an already non-stoichiometric system becomes progressively more favourable, which indicates the stability of the highly non-stoichiometric interfaces. Isolated water molecules dissociate when adsorbed at the TiO<sub>2</sub> layers. At higher coverages the preference is for molecular water adsorption. Our ab initio thermodynamics calculations show the fully water covered stoichiometric models as the most stable structure at typical ambient conditions. Interfacial models with multiple vacancies are most stable at low (reducing) oxygen chemical potential values. A water monolayer adsorbs dissociatively on the highly distorted 2-layer TiO<sub>1.75</sub>-TiN interface, where the Ti<sup>3+</sup> states lying above the top of the valence band contribute to a significant reduction of the energy gap compared to the stoichiometric TiO<sub>2</sub>-TiN model. Our results provide a guide for the design of novel interfacial systems containing ultrathin TiO<sub>2</sub> with potential application as photocatalytic water splitting devices.</p><p></p>

Applications of random graphs

2017 ◽  
Author(s):  
A.C.C. Coolen ◽  
A. Annibale ◽  
E.S. Roberts
Keyword(s):  
Social Networks ◽  
Random Graphs ◽  
Interaction Network ◽  
Power Grids ◽  
Protein Protein Interaction ◽  
Topological Features ◽  
First Case ◽  
The Stability ◽  
Protein Protein Interaction Network

This chapter reviews graph generation techniques in the context of applications. The first case study is power grids, where proposed strategies to prevent blackouts have been tested on tailored random graphs. The second case study is in social networks. Applications of random graphs to social networks are extremely wide ranging – the particular aspect looked at here is modelling the spread of disease on a social network – and how a particular construction based on projecting from a bipartite graph successfully captures some of the clustering observed in real social networks. The third case study is on null models of food webs, discussing the specific constraints relevant to this application, and the topological features which may contribute to the stability of an ecosystem. The final case study is taken from molecular biology, discussing the importance of unbiased graph sampling when considering if motifs are over-represented in a protein–protein interaction network.

State-dependent signalling in queueing networks

1994 ◽  
Vol 26 (02) ◽  
pp. 436-455 ◽  
Author(s):  
W. Henderson ◽  
B. S. Northcote ◽  
P. G. Taylor
Keyword(s):  
Queueing Networks ◽  
State Dependence ◽  
Product Form ◽  
Batch Size ◽  
Single Server ◽  
Negative Customers ◽  
Affect Control ◽  
State Dependent ◽  
Special Cases ◽  
Equilibrium Distributions

It has recently been shown that networks of queues with state-dependent movement of negative customers, and with state-independent triggering of customer movement have product-form equilibrium distributions. Triggers and negative customers are entities which, when arriving to a queue, force a single customer to be routed through the network or leave the network respectively. They are ‘signals' which affect/control network behaviour. The provision of state-dependent intensities introduces queues other than single-server queues into the network. This paper considers networks with state-dependent intensities in which signals can be either a trigger or a batch of negative customers (the batch size being determined by an arbitrary probability distribution). It is shown that such networks still have a product-form equilibrium distribution. Natural methods for state space truncation and for the inclusion of multiple customer types in the network can be viewed as special cases of this state dependence. A further generalisation allows for the possibility of signals building up at nodes.

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