Busy period distribution in state-dependent queues

1987 ◽  
Vol 2 (3) ◽  
pp. 285-305 ◽  
Author(s):  
C. Knessl ◽  
B. J. Matkowsky ◽  
Z. Schuss ◽  
C. Tier
Keyword(s):  
Busy Period ◽  
Period Distribution ◽  
State Dependent

Analysis of state-dependent discrete-time queue with system disaster

2019 ◽  
Vol 53 (5) ◽  
pp. 1915-1927
Author(s):  
Ramupillai Sudhesh ◽  
Arumugam Vaithiyanathan
Keyword(s):  
Discrete Time ◽  
Busy Period ◽  
System Size ◽  
Time Dependent ◽  
System Effect ◽  
Period Distribution ◽  
State Dependent ◽  
Discrete Time Queue ◽  
Formal Power ◽  
Time Dependent System

An explicit expression for time-dependent system size probabilities is obtained for the general state-dependent discrete-time queue with system disaster. Using generating function for the nth state transient probabilities, the underlying difference equation of system size probabilities are transformed into three-term recurrence relation which is then expressed as a continued fraction. The continued fractions are converted into formal power series which yield the time-dependent system size probabilities in closed form. Further, the busy period distribution is obtained for the considered model. As a special case, the system size probabilities and busy period distribution of Geo/Geo/1 queue are deduced. Finally, numerical illustrations are presented to visualize the system effect for various values of the parameters.

scholarly journals Single server queues with modified service mechanisms

1962 ◽  
Vol 2 (4) ◽  
pp. 499-507 ◽  
Author(s):  
G. F. Yeo
Keyword(s):  
Time Distribution ◽  
Busy Period ◽  
Queueing System ◽  
Probability Generating Function ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Period Distribution ◽  
Time Dependent Problem ◽  
Stationary Waiting Time ◽  
Special Case

SummaryThis paper considers a generalisation of the queueing system M/G/I, where customers arriving at empty and non-empty queues have different service time distributions. The characteristic function (c.f.) of the stationary waiting time distribution and the probability generating function (p.g.f.) of the queue size are obtained. The busy period distribution is found; the results are generalised to an Erlangian inter-arrival distribution; the time-dependent problem is considered, and finally a special case of server absenteeism is discussed.

AN EMERGENCY FACILITY WITH MINIMAL ADMISSION

2002 ◽  
Vol 16 (4) ◽  
pp. 499-511
Author(s):  
J. Preater
Keyword(s):  
Busy Period ◽  
Heavy Traffic ◽  
Queuing System ◽  
Period Distribution

We study an M/M/∞ queuing system in which each arrival has a random urgency and is admitted if and only if it is more urgent than all individuals currently receiving service. The system represents, for example, a less-than-magnanimous emergency facility. For this system, and also for a closely related “Parody,” we study the busy period distribution and, to a lesser extent, occupancy. Both exact and heavy traffic results are given.

On the busy period distribution of the M/G/2 queueing system

1989 ◽  
Vol 26 (04) ◽  
pp. 858-865 ◽  
Author(s):  
Douglas P. Wiens
Keyword(s):  
Linear Combination ◽  
Busy Period ◽  
Queueing System ◽  
Rate Parameter ◽  
Period Distribution ◽  
Special Cases ◽  
Service Times ◽  
Arbitrary Linear Combination

Equations are derived for the distribution of the busy period of the GI/G/2 queue. The equations are analyzed for the M/G/2 queue, assuming that the service times have a density which is an arbitrary linear combination, with respect to both the number of stages and the rate parameter, of Erlang densities. The coefficients may be negative. Special cases and examples are studied.

Busy period analysis of the state dependent M/M/1/K queue

2010 ◽  
Vol 38 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Ahmad Al Hanbali ◽  
Onno Boxma
Keyword(s):  
Busy Period ◽  
The State ◽  
Period Analysis ◽  
State Dependent

The stable M/G/1 queue in heavy traffic and its covariance function

1977 ◽  
Vol 9 (01) ◽  
pp. 169-186 ◽  
Author(s):  
Teunis J. Ott
Keyword(s):  
Brownian Motion ◽  
Waiting Time ◽  
Covariance Function ◽  
Busy Period ◽  
Stationary Process ◽  
Heavy Traffic ◽  
Time Process ◽  
Period Distribution ◽  
Virtual Waiting Time ◽  
Waiting Time Process

Let X(t) be the virtual waiting-time process of a stable M/G/1 queue. Let R(t) be the covariance function of the stationary process X(t), B(t) the busy-period distribution of X(t); and let E(t) = P{X(t) = 0|X(0) = 0}. For X(t) some heavy-traffic results are given, among which are limiting expressions for R(t) and its derivatives and for B(t) and E(t). These results are used to find the covariance function of stationary Brownian motion on [0, ∞).

Sign in / Sign up

Export Citation Format

Share Document