scholarly journals Age of Information in a Cooperative Slotted Aloha Network: Marginal and Joint Distributions

2021 ◽  
Author(s):  
Kaveh Vaezi ◽  
Nail Akar ◽  
Ezhan Karasan
Keyword(s):  
Steady State ◽  
Relay Node ◽  
Cooperative Network ◽  
Slotted Aloha ◽  
Steady State Distribution ◽  
State Distribution ◽  
Joint Distributions ◽  
Markov Chain Models ◽  
Cooperation Policy ◽  
Age Of Information

In this paper, we investigate a slotted Aloha cooperative network where a source node and a relay node send status updates of two underlying stochastic processes to a common destination. Additionally, the relay node cooperates with the source by accepting its packets for further retransmissions, where the cooperation policy comprises acceptance and relaying probabilistic policies. Exact marginal steady state distributions of the source and relay Age of Information (AoI) and Peak AoI (PAoI) sequences are obtained using Quasi-Birth-Death (QBD) Markov chain models. Extending this approach, we also obtain the joint distribution of the source and relay AoI sequences out of which one can obtain the steady state distribution of the Squared Difference of the two AoI sequences (SDAoI), which finds applications in network scenarios where not only the timeliness of status updates of each process is desired but also their simultaneity is of crucial importance. In this regard, we numerically obtain the optimal cooperation policy in order to minimize the expected value of SDAoI subject to a constraint on the average PAoI of the relay. Finally, our proposed analytical approach is verified by simulations and the performance of the optimal policy is discussed based on the numerical results.

scholarly journals Age of Information in a Cooperative Slotted Aloha Network: Marginal and Joint Distributions

2021 ◽  
Author(s):  
Kaveh Vaezi ◽  
Nail Akar ◽  
Ezhan Karasan
Keyword(s):  
Steady State ◽  
Relay Node ◽  
Cooperative Network ◽  
Slotted Aloha ◽  
Steady State Distribution ◽  
State Distribution ◽  
Joint Distributions ◽  
Markov Chain Models ◽  
Cooperation Policy ◽  
Age Of Information

In this paper, we investigate a slotted Aloha cooperative network where a source node and a relay node send status updates of two underlying stochastic processes to a common destination. Additionally, the relay node cooperates with the source by accepting its packets for further retransmissions, where the cooperation policy comprises acceptance and relaying probabilistic policies. Exact marginal steady state distributions of the source and relay Age of Information (AoI) and Peak AoI (PAoI) sequences are obtained using Quasi-Birth-Death (QBD) Markov chain models. Extending this approach, we also obtain the joint distribution of the source and relay AoI sequences out of which one can obtain the steady state distribution of the Squared Difference of the two AoI sequences (SDAoI), which finds applications in network scenarios where not only the timeliness of status updates of each process is desired but also their simultaneity is of crucial importance. In this regard, we numerically obtain the optimal cooperation policy in order to minimize the expected value of SDAoI subject to a constraint on the average PAoI of the relay. Finally, our proposed analytical approach is verified by simulations and the performance of the optimal policy is discussed based on the numerical results.

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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