On the Busy Periods of Single-Server Queues with Poisson Input and General Service Times

1976 ◽  
Vol 24 (3) ◽  
pp. 564-571 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Single Server ◽  
Single Server Queues ◽  
Poisson Input ◽  
General Service Times ◽  
Service Times ◽  
General Service

A single-server queue with limited virtual waiting time

1974 ◽  
Vol 11 (03) ◽  
pp. 612-617 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Waiting Time ◽  
Single Server ◽  
Single Server Queue ◽  
Limiting Distributions ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
General Service Times ◽  
Server Queue ◽  
Service Times ◽  
General Service

The limiting distributions of the actual waiting time and the virtual waiting time are determined for a single-server queue with Poisson input and general service times in the case where there are two types of services and no customer can stay in the system longer than an interval of length m.

A single-server queue with limited virtual waiting time

1974 ◽  
Vol 11 (3) ◽  
pp. 612-617 ◽  
Author(s):  
Lajos Takács
Keyword(s):  
Waiting Time ◽  
Single Server ◽  
Single Server Queue ◽  
Limiting Distributions ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
General Service Times ◽  
Server Queue ◽  
Service Times ◽  
General Service

The limiting distributions of the actual waiting time and the virtual waiting time are determined for a single-server queue with Poisson input and general service times in the case where there are two types of services and no customer can stay in the system longer than an interval of length m.

A queueing system with impatient customers

1985 ◽  
Vol 22 (3) ◽  
pp. 688-696 ◽  
Author(s):  
A. G. De Kok ◽  
H. C. Tijms
Keyword(s):  
Performance Measures ◽  
Queueing System ◽  
Fixed Time ◽  
Single Server ◽  
Impatient Customers ◽  
Average Delay ◽  
Practical Applications ◽  
Poisson Input ◽  
General Service Times ◽  
General Service

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.

scholarly journals Covert Cycle Stealing in a Single FIFO Server

2021 ◽  
Vol 6 (2) ◽  
pp. 1-33
Author(s):  
Bo Jiang ◽  
Philippe Nain ◽  
Don Towsley
Keyword(s):  
Phase Transition ◽  
Fisher Information ◽  
Single Server ◽  
Expected Number ◽  
General Service Times ◽  
Poisson Stream ◽  
Service Times ◽  
First In First Out ◽  
To Receive ◽  
General Service

Consider a setting where Willie generates a Poisson stream of jobs and routes them to a single server that follows the first-in first-out discipline. Suppose there is an adversary Alice, who desires to receive service without being detected. We ask the question: What is the number of jobs that she can receive covertly, i.e., without being detected by Willie? In the case where both Willie and Alice jobs have exponential service times with respective rates μ 1 and μ 2 , we demonstrate a phase-transition when Alice adopts the strategy of inserting a single job probabilistically when the server idles: over n busy periods, she can achieve a covert throughput, measured by the expected number of jobs covertly inserted, of O (√ n ) when μ 1 < 2 μ 2 , O (√ n log n ) when μ 1 = 2μ 2 , and O ( n μ 2 /μ 1 ) when μ 1 > 2μ 2 . When both Willie and Alice jobs have general service times, we establish an upper bound for the number of jobs Alice can execute covertly. This bound is related to the Fisher information. More general insertion policies are also discussed.

Asymptotic transient behaviour of the bulk service queue

1963 ◽  
Vol 3 (4) ◽  
pp. 503-512 ◽  
Author(s):  
B. D. Craven
Keyword(s):  
Service Time ◽  
Single Server ◽  
Transient Behaviour ◽  
Single Server Queues ◽  
Poisson Input ◽  
Bulk Service ◽  
Service Times

Various authors have studied the transient behaviour of single-server queues. Notably, Takacs [13], [14] has analysed a queue with recurrent input and exponential service time distributions, Keilson and Kooharian [9], [10] and Finch [5] have considered a queue with general independent input and service times, Finch [6] has analysed a queue with non-recurrent input and Erlang service, and Jaiswal [8] has considered the bulk-service queue with Poisson input and Erlang service.

scholarly journals On A Single Server Queue with Two-Stage First Essential Service Followed by One of the Two Types of Additional Optional Service and Optional Deterministic Server Vacations

2021 ◽  
Vol 15 ◽  
pp. 1730-1736
Author(s):  
Kailash C. Madan
Keyword(s):  
Steady State ◽  
Single Server ◽  
Single Server Queue ◽  
Optional Service ◽  
General Service Times ◽  
Server Queue ◽  
Service Times ◽  
Two Stages ◽  
General Service ◽  
Essential Service

We study the steady state behavior of a batch arrival single server queue in which the first service consisting of two stages with general service times G1 and G2 is compulsory. After completion of the two stages of the first essential service, a customer has the option of choosing one of the two types of additional service with respective general service times G1 and G2 . Just after completing both stages of first essential service with or without one of the two types of additional optional service, the server has the choice of taking an optional deterministic vacation of fixed (constant) length of time. We obtain steady state probability generating functions for the queue size for various states of the system at a random epoch of time in explicit and closed forms. The steady state results of some interesting special cases have been derived from the main results.

A queueing system with impatient customers

1985 ◽  
Vol 22 (03) ◽  
pp. 688-696 ◽  
Author(s):  
A. G. De Kok ◽  
H. C. Tijms
Keyword(s):  
Performance Measures ◽  
Queueing System ◽  
Fixed Time ◽  
Single Server ◽  
Impatient Customers ◽  
Average Delay ◽  
Practical Applications ◽  
Poisson Input ◽  
General Service Times ◽  
General Service

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.

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