The M/M/∞ queue in a random environment

1986 ◽  
Vol 23 (1) ◽  
pp. 175-184 ◽  
Author(s):  
C. A. O'Cinneide ◽  
P. Purdue
Keyword(s):  
Steady State ◽  
Random Environment ◽  
Steady State Distribution ◽  
State Distribution ◽  
State Behavior ◽  
Factorial Moments ◽  
Numerical Examples ◽  
Server Queue ◽  
Service Rates ◽  
Steady State Behavior

The M/M/∞ queue in a random environment is an infinite-server queue where arrival and service rates are stochastic processes. Here we study the steady-state behavior of such a system. Explicit results are obtained for the factorial moments, the impossibility of a ‘matrix-Poisson' steady-state distribution is demonstrated and two numerical examples are presented.

The M/M /∞ queue in a random environment

1986 ◽  
Vol 23 (01) ◽  
pp. 175-184
Author(s):  
C. A. O'Cinneide ◽  
P. Purdue
Keyword(s):  
Steady State ◽  
Random Environment ◽  
Steady State Distribution ◽  
State Distribution ◽  
State Behavior ◽  
Factorial Moments ◽  
Numerical Examples ◽  
Server Queue ◽  
Service Rates ◽  
Steady State Behavior

The M/M/∞ queue in a random environment is an infinite-server queue where arrival and service rates are stochastic processes. Here we study the steady-state behavior of such a system. Explicit results are obtained for the factorial moments, the impossibility of a ‘matrix-Poisson' steady-state distribution is demonstrated and two numerical examples are presented.

BALKING AND RENEGING IN M/G/s SYSTEMS EXACT ANALYSIS AND APPROXIMATIONS

2008 ◽  
Vol 22 (3) ◽  
pp. 355-371 ◽  
Author(s):  
Liqiang Liu ◽  
Vidyadhar G. Kulkarni
Keyword(s):  
Steady State ◽  
Single Server ◽  
Impatient Customers ◽  
Operating Characteristics ◽  
Steady State Distribution ◽  
State Distribution ◽  
Numerical Examples ◽  
Exact Analysis ◽  
Analytical Results ◽  
Server System

We consider the virtual queuing time (vqt, also known as work-in-system, or virtual-delay) process in an M/G/s queue with impatient customers. We focus on the vqt-based balking model and relate it to reneging behavior of impatient customers in terms of the steady-state distribution of the vqt process. We construct a single-server system, analyze its operating characteristics, and use them to approximate the multiserver system. We give both analytical results and numerical examples. We conduct simulation to assess the accuracy of the approximation.

scholarly journals Correlation formulas for Markovian network processes in a random environment

2016 ◽  
Vol 48 (1) ◽  
pp. 176-198 ◽  
Author(s):  
Hans Daduna ◽  
Ryszard Szekli
Keyword(s):  
Steady State ◽  
Random Environment ◽  
Queueing Network ◽  
Correlation Structure ◽  
Time Behaviour ◽  
Spectral Gaps ◽  
Steady State Distribution ◽  
State Distribution ◽  
One Step ◽  
Asymptotic Variances

Abstract We consider Markov processes, which describe, e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit steady-state distribution of product form available in the literature, we note that this steady-state distribution does not provide information about the correlation structure in time and space (over nodes). We study this correlation structure via one-step correlations for the queueing-environment process. Although formulas for absolute values of these correlations are complicated, the differences of correlations of related networks are simple and have a nice structure. We therefore compare two networks in a random environment having the same invariant distribution, and focus on the time behaviour of the processes when in such a network the environment changes or the rules for travelling are perturbed. Evaluating the comparison formulas we compare spectral gaps and asymptotic variances of related processes.

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.

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