On Growth-Collapse Processes with Stationary Structure and Their Shot-Noise Counterparts

2009 ◽  
Vol 46 (2) ◽  
pp. 363-371 ◽  
Author(s):  
Offer Kella
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Growth Process ◽  
Initial Conditions ◽  
Steady State Distribution ◽  
State Distribution ◽  
Stationary Structure ◽  
Stationary Version ◽  
Special Cases ◽  
The Times

In this paper we generalize existing results for the steady-state distribution of growth-collapse processes. We begin with a stationary setup with some relatively general growth process and observe that, under certain expected conditions, point- and time-stationary versions of the processes exist as well as a limiting distribution for these processes which is independent of initial conditions and necessarily has the marginal distribution of the stationary version. We then specialize to the cases where an independent and identically distributed (i.i.d.) structure holds and where the growth process is a nondecreasing Lévy process, and in particular linear, and the times between collapses form an i.i.d. sequence. Known results can be seen as special cases, for example, when the inter-collapse times form a Poisson process or when the collapse ratio is deterministic. Finally, we comment on the relation between these processes and shot-noise type processes, and observe that, under certain conditions, the steady-state distribution of one may be directly inferred from the other.

On Growth-Collapse Processes with Stationary Structure and Their Shot-Noise Counterparts

2009 ◽  
Vol 46 (02) ◽  
pp. 363-371 ◽  
Author(s):  
Offer Kella
Keyword(s):  
Steady State ◽  
Shot Noise ◽  
Growth Process ◽  
Initial Conditions ◽  
Steady State Distribution ◽  
State Distribution ◽  
Stationary Structure ◽  
Stationary Version ◽  
Special Cases ◽  
The Times

In this paper we generalize existing results for the steady-state distribution of growth-collapse processes. We begin with a stationary setup with some relatively general growth process and observe that, under certain expected conditions, point- and time-stationary versions of the processes exist as well as a limiting distribution for these processes which is independent of initial conditions and necessarily has the marginal distribution of the stationary version. We then specialize to the cases where an independent and identically distributed (i.i.d.) structure holds and where the growth process is a nondecreasing Lévy process, and in particular linear, and the times between collapses form an i.i.d. sequence. Known results can be seen as special cases, for example, when the inter-collapse times form a Poisson process or when the collapse ratio is deterministic. Finally, we comment on the relation between these processes and shot-noise type processes, and observe that, under certain conditions, the steady-state distribution of one may be directly inferred from the other.

Algorithms for a continuous-review (s, S) inventory system

1981 ◽  
Vol 18 (02) ◽  
pp. 461-472
Author(s):  
V. Ramaswami
Keyword(s):  
Steady State ◽  
Inventory System ◽  
Steady State Distribution ◽  
State Distribution ◽  
Continuous Review ◽  
Markov Modulated Poisson Process ◽  
Special Cases ◽  
Phase Type ◽  
Markov Modulated ◽  
Stimulation Of

The steady-state distribution of the inventory position for a continuous-review (s, S) inventory system is derived in a computationally tractable form. Demands for items in inventory are assumed to form an N-process which is the ‘versatile Markovian point process' introduced by Neuts (1979). The N-process includes the phase-type renewal process, Markov-modulated Poisson process etc., as special cases and is especially useful in modelling a wide variety of qualitative phenomena such as peaked arrivals, interruptions, inhibition or stimulation of arrivals by certain events etc.

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.

scholarly journals Tail Asymptotics for a Random Sign Lindley Recursion

2010 ◽  
Vol 47 (01) ◽  
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.

Algorithms for a continuous-review (s, S) inventory system

1981 ◽  
Vol 18 (2) ◽  
pp. 461-472 ◽  
Author(s):  
V. Ramaswami
Keyword(s):  
Steady State ◽  
Inventory System ◽  
Steady State Distribution ◽  
State Distribution ◽  
Continuous Review ◽  
Markov Modulated Poisson Process ◽  
Special Cases ◽  
Phase Type ◽  
Markov Modulated ◽  
Stimulation Of

The steady-state distribution of the inventory position for a continuous-review (s, S) inventory system is derived in a computationally tractable form. Demands for items in inventory are assumed to form an N-process which is the ‘versatile Markovian point process' introduced by Neuts (1979). The N-process includes the phase-type renewal process, Markov-modulated Poisson process etc., as special cases and is especially useful in modelling a wide variety of qualitative phenomena such as peaked arrivals, interruptions, inhibition or stimulation of arrivals by certain events etc.

Kinetic analysis of mechanism of intestinal Na+-dependent sugar transport

1985 ◽  
Vol 248 (5) ◽  
pp. C498-C509 ◽  
Author(s):  
D. Restrepo ◽  
G. A. Kimmich
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Sugar Transport ◽  
Enzyme Kinetic ◽  
Steady State Distribution ◽  
State Distribution ◽  
Least Squares Fit ◽  
Coupling Stoichiometry ◽  
Rate Limiting ◽  
Kinetics Of

Zero-trans kinetics of Na+-sugar cotransport were investigated. Sugar influx was measured at various sodium and sugar concentrations in K+-loaded cells treated with rotenone and valinomycin. Sugar influx follows Michaelis-Menten kinetics as a function of sugar concentration but not as a function of Na+ concentration. Nine models with 1:1 or 2:1 sodium:sugar stoichiometry were considered. The flux equations for these models were solved assuming steady-state distribution of carrier forms and that translocation across the membrane is rate limiting. Classical enzyme kinetic methods and a least-squares fit of flux equations to the experimental data were used to assess the fit of the different models. Four models can be discarded on this basis. Of the remaining models, we discard two on the basis of the trans sodium dependence and the coupling stoichiometry [G. A. Kimmich and J. Randles, Am. J. Physiol. 247 (Cell Physiol. 16): C74-C82, 1984]. The remaining models are terter ordered mechanisms with sodium debinding first at the trans side. If transfer across the membrane is rate limiting, the binding order can be determined to be sodium:sugar:sodium.

PROCESSOR SHARING G-QUEUES WITH INERT CUSTOMERS AND CATASTROPHES: A MODEL FOR SERVER AGING AND REJUVENATION

2017 ◽  
Vol 31 (4) ◽  
pp. 420-435 ◽  
Author(s):  
J.-M. Fourneau ◽  
Y. Ait El Majhoub
Keyword(s):  
Steady State ◽  
Product Form ◽  
Processor Sharing ◽  
Service Capacity ◽  
Steady State Distribution ◽  
State Distribution ◽  
Signal Arrival ◽  
Open Networks ◽  
Networks Of Queues

We consider open networks of queues with Processor-Sharing discipline and signals. The signals deletes all the customers present in the queues and vanish instantaneously. The customers may be usual customers or inert customers. Inert customers do not receive service but the servers still try to share the service capacity between all the customers (inert or usual). Thus a part of the service capacity is wasted. We prove that such a model has a product-form steady-state distribution when the signal arrival rates are positive.

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