398 research outputs found
On the GI/M/1/N queue with multiple working vacations—analytic analysis and computation
AbstractWe consider finite buffer single server GI/M/1 queue with exhaustive service discipline and multiple working vacations. Service times during a service period, service times during a vacation period and vacation times are exponentially distributed random variables. System size distributions at pre-arrival and arbitrary epoch with some important performance measures such as, probability of blocking, mean waiting time in the system etc. have been obtained. The model has potential application in the area of communication network, computer systems etc. where a single channel is allotted for more than one source
Analysis and optimization of vacation and polling models with retrials
We study a vacation-type queueing model, and a single-server multi-queue
polling model, with the special feature of retrials. Just before the server
arrives at a station there is some deterministic glue period. Customers (both
new arrivals and retrials) arriving at the station during this glue period will
be served during the visit of the server. Customers arriving in any other
period leave immediately and will retry after an exponentially distributed
time. Our main focus is on queue length analysis, both at embedded time points
(beginnings of glue periods, visit periods and switch- or vacation periods) and
at arbitrary time points.Comment: Keywords: vacation queue, polling model, retrials Submitted for
review to Performance evaluation journal, as an extended version of 'Vacation
and polling models with retrials', by Onno Boxma and Jacques Resin
STEADY-STATE ANALYSIS OF THE GI/M/1 QUEUE WITH MULTIPLE VACATIONS AND SET-UP TIME
In this paper, we consider a GI/M/1 queueing model with multiple vacations and set-up time. We derive the distribution and the generating function and the stochastic decomposition of the steady-state queue length, meanwhile, we get the waiting time distributions. Key words: multiple vacations, set-up time, stochastic decompositio
Sleep Mode Analysis via Workload Decomposition
The goal of this paper is to establish a general approach for analyzing
queueing models with repeated inhomogeneous vacations. The server goes on for a
vacation if the inactivity prolongs more than the vacation trigger duration.
Once the system enters in vacation mode, it may continue for several
consecutive vacations. At the end of a vacation, the server goes on another
vacation, possibly with a different probability distribution; if during the
previous vacation there have been no arrivals. However the system enters in
vacation mode only if the inactivity is persisted beyond defined trigger
duration. In order to get an insight on the influence of parameters on the
performance, we choose to study a simple M/G/1 queue (Poisson arrivals and
general independent service times) which has the advantage of being tractable
analytically. The theoretical model is applied to the problem of power saving
for mobile devices in which the sleep durations of a device correspond to the
vacations of the server. Various system performance metrics such as the frame
response time and the economy of energy are derived. A constrained optimization
problem is formulated to maximize the economy of energy achieved in power save
mode, with constraints as QoS conditions to be met. An illustration of the
proposed methods is shown with a WiMAX system scenario to obtain design
parameters for better performance. Our analysis allows us not only to optimize
the system parameters for a given traffic intensity but also to propose
parameters that provide the best performance under worst case conditions
Another look into decomposition results
In this note, we identify a simple setup from which one may easily infer various decomposition results for queues with interruptions as well as càdlàg processes with certain secondary jump inputs. Special cases are processes with stationary or stationary and independent increments. In the Lévy process case, the decomposition holds not only in the limit but also at independent exponential times, due to the Wiener-Hopf decomposition. A similar statement holds regarding the GI/GI/1 setting with multiple vacation
Exact Solutions for M/M/c/Setup Queues
Recently multiserver queues with setup times have been extensively studied
because they have applications in power-saving data centers. The most
challenging model is the M/M//Setup queue where a server is turned off when
it is idle and is turned on if there are some waiting jobs. Recently, Gandhi et
al.~(SIGMETRICS 2013, QUESTA 2014) present the recursive renewal reward
approach as a new mathematical tool to analyze the model. In this paper, we
derive exact solutions for the same model using two alternative methodologies:
generating function approach and matrix analytic method. The former yields
several theoretical insights into the systems while the latter provides an
exact recursive algorithm to calculate the joint stationary distribution and
then some performance measures so as to give new application insights.Comment: Submitted for revie
- …