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.

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 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.

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.

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.

Diffusion approximations for queues with server vacations

1990 ◽  
Vol 22 (3) ◽  
pp. 706-729 ◽  
Author(s):  
Offer Kella ◽  
Ward Whitt
Keyword(s):  
Brownian Motion ◽  
Steady State ◽  
Heavy Traffic ◽  
Service Discipline ◽  
Single Server ◽  
Traffic Intensity ◽  
Steady State Distribution ◽  
State Distribution ◽  
Reflecting Brownian Motion ◽  
Heavy Traffic Limit

This paper studies the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, modified by having the server take random vacations. In the first model, there is a vacation each time the queue becomes empty, as occurs for high-priority customers with a non-preemptive priority service discipline. Approximations for both the transient and steady-state behavior are developed for the case of relatively long vacations by proving a heavy-traffic limit theorem. If the vacation times increase appropriately as the traffic intensity increases, the workload and queue-length processes converge in distribution to Brownian motion with a negative drift, modified to have a random jump up whenever it hits the origin. In the second model, vacations are generated exogenously. In this case, if both the vacation times and the times between vacations increase appropriately as the traffic intensity increases, then the limit process is reflecting Brownian motion, modified by the addition of an exogenous jump process. The steady-state distributions of these two limiting jump-diffusion processes have decomposition properties previously established for vacation queueing models, i.e., in each case the steady-state distribution is the convolution of two distributions, one of which is the exponential steady-state distribution of the reflecting Brownian motion obtained as the heavy-traffic limit without vacations.

Diffusion approximations for queues with server vacations

1990 ◽  
Vol 22 (03) ◽  
pp. 706-729 ◽  
Author(s):  
Offer Kella ◽  
Ward Whitt
Keyword(s):  
Brownian Motion ◽  
Steady State ◽  
Heavy Traffic ◽  
Service Discipline ◽  
Single Server ◽  
Traffic Intensity ◽  
Steady State Distribution ◽  
State Distribution ◽  
Reflecting Brownian Motion ◽  
Heavy Traffic Limit

This paper studies the standard single-server queue with unlimited waiting space and the first-in first-out service discipline, modified by having the server take random vacations. In the first model, there is a vacation each time the queue becomes empty, as occurs for high-priority customers with a non-preemptive priority service discipline. Approximations for both the transient and steady-state behavior are developed for the case of relatively long vacations by proving a heavy-traffic limit theorem. If the vacation times increase appropriately as the traffic intensity increases, the workload and queue-length processes converge in distribution to Brownian motion with a negative drift, modified to have a random jump up whenever it hits the origin. In the second model, vacations are generated exogenously. In this case, if both the vacation times and the times between vacations increase appropriately as the traffic intensity increases, then the limit process is reflecting Brownian motion, modified by the addition of an exogenous jump process. The steady-state distributions of these two limiting jump-diffusion processes have decomposition properties previously established for vacation queueing models, i.e., in each case the steady-state distribution is the convolution of two distributions, one of which is the exponential steady-state distribution of the reflecting Brownian motion obtained as the heavy-traffic limit without vacations.

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.

Sign in / Sign up

Export Citation Format

Share Document