The sliding window algorithm proposed for determining an optimal sliding window does not consider the waiting times of call setup requests of a mobile station in queue at a Mobile Switching Centre (MSC) in the Global System for Mobile (GSM) Communication Network. This study proposes a model integrating the sliding window algorithm with a single server finite queuing model, referred to as integrated model for measurement of realistic throughput of a MSC considering the waiting times of call setup requests. It assumes that a MSC can process one call setup request at a time. It is useful in determining an optimal sliding window size that maximizes the realistic throughput of a MSC. Though the model assumes that a MSC can process one call setup request at a time, its scope can be extended for measuring the realistic throughput of a MSC that can process multiple call setup requests at a time.
A mobile subscriber is uniquely identified by Mobile Station International Subscriber Directory Number (MSISDN) in the Global System for Mobile (GSM) Communication Network. The GSM network provides services to its registered mobile subscribers using the Gateway Mobile Switching Centre (GMSC) of a service provider. The GMSC area is partitioned into several areas with a switching centre at each area referred to as Mobile Switching Centre (MSC) connected to GMSC. The profiles of mobile subscribers are stored persistently in Home Location Register (HLR) at GMSC. Each MSC maintains a Visitor Location Register (VLR), which stores the profiles of mobile subscribers temporarily [
The mobile subscribers roam randomly in the GSM network area. It is observed that the policy of accessing HLR is fetching the profile of a mobile subscriber to VLR whenever it arrives at MSC service area and deleting the same whenever it leaves. This method increases the load on the network traffic, delays call setup time, and reduces the throughput of MSC [
At the end of each day beyond initial seven days, the model determines the intersection of mobile subscribers’ profiles over seven slots, slides the window by one slot right masking the front slot and opening new slot at the other end, and copies the intersection to newly opened slot.
A simulation model is developed for evaluating the performance of FBSD and SWSSD algorithms. The analysis of simulation output proved that the SWSSD algorithm is better than the existing FBSD algorithm as it decreases the average call setup time by 6.28% and increases the throughput by 7.08%. Further, Nuka and Naidu [
However, the SWSSD algorithm [
The paper is divided into 8 sections inclusive of this section. In Section
GSM network system is portioned into three subsystems, namely, Base Station Subsystem (BSS), Network Switching Subsystem (NSS), and Operational Subsystem (OSS) as shown in Figure
GSM network architecture.
The profiles of all the mobile subscribers registered with a service provider are maintained using a centralized database at GMSC referred to as HLR. Whenever a MSC receives call setup request from a mobile subscriber through the BSS, it processes it for providing call setup services. The availability of profile of mobile subscriber at the MSC is necessary for processing the call setup request. To meet this prerequisite, at each MSC a database, referred to as VLR, is maintained for storing temporarily the profiles of mobile subscribers which are currently in the service area of a MSC. One extreme policy is replicating the HLR as VLR at each MSC. This policy increases throughput of a MSC while increasing the cost of storage. Other extreme policy is fetching the profile whenever the mobile subscriber enters the location area and deleting the same on its exit. This policy decreases the throughput of MSC while increasing network traffic overhead. Hence, it is essential to undertake the problem for determining the retention period of the profiles of mobile subscribers in VLR in spite of leaving the service area of a MSC with the objective of maximizing the throughput of MSC while minimizing the sum of the costs of storage and network traffic overhead.
The review of related work reported in [
However, the SWSSD algorithm [
A model proposed in [
The SWSSD algorithm has been proposed for determining the holding period of a record of a mobile subscriber profile in VLR, instead of deleting immediately when the mobile subscriber leaves the service area of a MSC, with an objective of maximizing throughput of the MSC and minimizing call setup time [
On a given day, the MSISDNs made call setup requests which comprise one set of the sliding windows. Initially, the days are denoted by numbers one to seven and their corresponding sets are set to null. A set is updated applying union operation between the current set and a MSISDN from which the call setup request is received, provided the relevant record of the MSISDN is fetched from HLR due to nonavailability of the same in VLR. At end of the seventh day, the intersection of seven sets is determined. The set in the first position of sliding window is deleted by shifting other six sets left by one position. This is equivalent to sliding the window to right by one position. The intersection is copied in the seventh position of sliding window. Consequently, the days are incremented by one. Thereafter, at the end of each day, the tasks of determining the intersection, sliding the window, copying the intersection, and incrementing days are repeated over days. The definitions of notation are given below:
( ( ( ( ( (
( ( ( ( ( (
The inputs to CALLSETUP( ) procedure are MSISDN that represents call setup request and the day of request. If the condition in line (
In line (
A simulation model is developed for evaluating the performance of SWSSD algorithm [
( ( ( ( CR = Poison random variates that represents number of call setup requests for ( ( Generate a discrete uniform random variant “ ( ( Setup call ( (a) Fetch the profile of “ (b) Setup call (c) ( ( ( ( ( ( (
( ( Setup call ( (a) Fetch the profile of “ (b) Setup call (c) ( (
The metrics employed for evaluating the performance of the SWSSD algorithms are hit rate and throughput that shall be maximized.
The hit rate is the probability of the relevant record availability in VLR for processing a call setup request. The numbers of hits and call setup requests over a period of time are measured for computing hit rate. It is assumed that call setup requests are received randomly from a finite set of MSISDNs. The availability of relevant record of an MSISDN in VLR for processing its call setup request is referred to as a hit whereas nonavailability is referred to as a miss.
Throughput of a MSC is the number of call setups per unit time. The average call setup time for a call setup request is computed using
Obviously,
The reciprocal of average call setup time is throughput and the same is computed using
A simulation model is developed for evaluating the performance of SWSSD algorithm. It is used to generate the performance measures of SWSSD algorithm over a period of 1001 days. It is evident from the results that there is a significant increase in performance metrics of the proposed SWSSD algorithm for one MSC service area comparing with Fixed Block of Seven Days (FBSD) algorithm [
An entity that approaches a service facility for want of service is referred to as customer whereas the service facility is referred to as server. The service on arrival of a customer is commenced immediately provided the server is idle. Otherwise the customer has to wait in the queue until its turn. The six elements of a queuing model are interarrival, service times of customers, number of servers, queue discipline, maximum queue size, and calling population size.
The interarrival and service times of customers are probabilistic in nature following respective probabilistic distributions. The number of servers is either single or multiple. The identical multiple servers are arranged parallelly whereas the nonidentical multiple servers are arranged in tandem. The queue discipline specifies order in which the next customer is selected from the queue for providing service. The queue disciplines are First Come First Served (FCFS), Last Come First Served (LCFS), Selection in Random Order (SIRO), and order of priority. The maximum queue size is the maximum number of customers permitted to wait in queue. It is assumed as infinite whenever there is no restriction on queue size. The calling population size is assumed as infinite whenever it exceeds threshold.
A queuing model is descriptive in nature which provides the change of the state of a queuing system due to occurrence of customer arrival and departure events. The state of a queuing system is represented by the status of server (busy or idle), number of customers in system, and queue. As the arrival and departure events occur randomly over time, the state of the queuing system changes randomly.
The steady state performance measures of queuing system server utilization, mean number of customers in system/queue, and mean waiting time in system/queue can be computed. These measures are used in a cost model for deciding the number of servers and quality of service. All setup requests from mobile subscribers are customers whereas the MSC that can process one request at a time for providing call setup services is a server. Obviously, the number of mobile subscribers is finite. Hence, the queuing system under consideration is formulated as a single server finite queuing model.
The sliding window algorithm ensures minimum average call setup time which is termed as average service time of queuing system. However, the sliding window algorithm does not consider the waiting of call setup request while a MSC is busy.
The average waiting time in queue shall be added to average call setup time to determine the average time a call setup request spends at a MSC. For this purpose, sliding window algorithm is integrated with a single sever finite queuing model. Henceforth, it is referred to as an integrated model depicted in Figure
Integrated model.
It is assumed that the customer (call setup request) arrival rate follows Poisson distribution with parameter
Obviously, an analytical solution cannot be found for computing average waiting time of call setup requests in queue and it is to be determined through simulation.
The simulation of the integrated model generates an artificial history of system facilitating the measurement of throughput of a MSC. The entities considered for developing simulation model are mobile stations and Mobile Switching Centre. The mobile stations are represented by their unique identities, MSISDNs. The call setup requests from MSISDNs are the customers. The Mobile Switching Centre (MSC) is a server. A set of mobile stations registered with a service provider constitute the calling population source from which call setup requests are received.
In GSM network, the profiles of MSISDNs comprising several attributes are stored in HLR at Gateway Mobile Switching Centre (GMSC). The profiles of MSISDNs in the service area of a MSC are stored in VLR. Whenever an MSISDN profile is not available in VLR for processing its call setup request, its profile is fetched from HLR. The deletion of the profile of an MSISDN from VLR depends on the sliding window algorithm.
The metric employed evaluating the performance of a MSC using integrated model is throughput considering waiting time in queue would be more realistic. Equations (
Obviously,
The reciprocal of average waiting time in system is throughput shown in
The simulation is performed using TN3270 emulator for IBM (zSeries) mainframe on windows platform with z/OS IBM mainframe operating system and DB2 database server. The notations and input parameters of simulation are shown in Table
Simulation parameters.
Symbol | Description | Value |
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|
Simulation run length in days | 1001 |
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Calling population size | 88243 |
|
Ordered set of calling population |
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Parameter of Poisson distribution, that is, mean number of call setup requests per day | 87 |
1/ |
Parameter of exponential distribution | 0.02 |
|
Call setup time in case of record available in VLR | 3 |
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Call setup time in case of record unavailable in VLR | 7 |
WS | Sliding window size in days | 7 |
The output of simulation for 88243 call setup requests over 1001 days is presented in Table
Simulation results.
Call setup request number |
Call setup request attribute values | Service time attribute values | Arrival time |
Service begins |
Service |
Waiting time in queue |
Waiting time in system |
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Day |
MSISDN | Interarrival |
Hit |
Call setup time |
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1 | 1 | 65 | 93 | No | 7 | 0 | 0 | 7 | 0 | 7 |
2 | 1 | 73 | 41 | No | 7 | 93 | 93 | 100 | 7 | 14 |
3 | 1 | 23 | 22 | No | 7 | 134 | 134 | 141 | 100 | 107 |
4 | 1 | 47 | 48 | No | 7 | 156 | 156 | 163 | 141 | 148 |
5 | 1 | 74 | 87 | No | 7 | 204 | 204 | 211 | 163 | 171 |
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88242 | 1001 | 41 | 5 | Yes | 3 | 3298 | 3298 | 3301 | 3284 | 3287 |
88243 | 1001 | 17 | 29 | No | 7 | 3303 | 3303 | 3310 | 3301 | 3308 |
A discrete uniform random variate represents the attribute MSISDN and its interarrival time is a random variate from an exponential distribution with parameter
The SWSSD algorithm performs, whenever a subscriber arrives and makes a call setup request, the MSC checks its database to determine whether the record is available at its VLR. and If it is available, it returns “yes”; otherwise, it returns “no” shown in column (5). Accordingly, call setup service times are 3 and 7 for hit and miss, respectively, shown in column (
The arrival time (
The waiting time in queue (
Aggregated simulation results for each block.
Period/blocks | Call setup requests | Hits | Sliding window algorithm | Integrated model | |||
---|---|---|---|---|---|---|---|
Average call setup time | Throughput | Average waiting time in queue |
Average waiting time in system |
Throughput | |||
1–7 | 621 | 318 | 4.951691 | 0.2019 | 31.8776 | 31.9178 | 0.03133 |
8–14 | 549 | 262 | 5.091075 | 0.1964 | 39.1165 | 39.1621 | 0.02553 |
15–21 | 631 | 239 | 5.484945 | 0.1823 | 32.0570 | 32.1030 | 0.03115 |
22–28 | 616 | 244 | 5.415584 | 0.1846 | 31.5487 | 31.5957 | 0.03165 |
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988–994 | 638 | 241 | 5.489028 | 0.1821 | 33.5109 | 33.5501 | 0.02806 |
995–1001 | 629 | 206 | 5.689984 | 0.1757 | 31.9793 | 32.0445 | 0.03120 |
Waiting time in queue over 1001 days.
Waiting time in system over 1001 days.
Throughput over 1001 days.
Call setup time in system versus blocks at a MSC.
Throughput versus blocks at a MSC.
The performance metrics, average waiting time in queue (AWTQ) and average waiting time in system (AWTS) computed using (
It is evident that the throughput of the proposed integrated model which considers waiting time in queue at a MSC is decreased by 83.12% for a single-channel MSC; it is a realistic measurement of throughput.
This study has proposed a realistic model for measuring throughput of a MSC integrating the sliding window algorithm with a single server finite queuing model. The sliding window algorithm minimizes the average call setup processing time and a single server finite queuing model determines the average call setup request waiting time in the queue. Hence, the reciprocal of the sum of average call setup processing time and average call setup request waiting time in the queue is more realistic average throughput of a MSC under consideration. This model facilitates determining an optimal sliding window size.
However, the model assumes a MSC with a single channel for processing call setup requests. It is worth attempting to develop a model considering a MSC with multiple identical channels for processing concurrently multiple call setup requests for measuring still more realistic throughput of a MSC. Further, it facilitates formulating a cost model for determining an optimal number of channels with the criterion of maximizing throughput of a MSC. The study in this direction is under progress.
The authors have no competing interests.
The author of the article, Dinaker Babu Bollini, pursuing his doctoral programme from SV University, Tirupati, has conceptualized integrating queuing model with the Sliding Window of Seven Days Algorithm for investigating the effect of waiting times of call setup requests on throughput of a Mobile Switching Centre. The first co-author, Dr. Mannava Muniratnam Naidu, as supervisor of the doctoral work provided guidance in formulating and validating the conceptual simulation model, design of experiments, and analysis of simulation output. The second co-author, Dr. Mallikharjuna Rao Nuka, translated the conceptual simulation model into an operational simulation model and carried out the computer simulation.